More could be said but you might find this recent answer by u/Snapshot52 useful, as well as this previous answer of mine.

Current law student who has taken both Federal Indian Law and Native American Natural Resource Law (in school in Oklahoma) so I can shed some light on this.

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The first thing to understand about Federal Indian Law, and thus federal-tribal treaties, is that it concerns sovereignty (power / authority / jurisdiction to enforce law or regulate conduct on the land) rather than property (who actually has ownership of the land).

So, the short answer to your question is that the United States government owns all tribal land that has not been actually purchased back from the tribes legally. This is confusing, so bear with me.

Differing European nations employed differing means of dealing with indigenous peoples in the Americas. The English relied primarily on treaty-making and the United States, as successor to Great Britain in North America, decided to continue on with that tradition. In the early Republic, as evidenced by the Treaty of Hopewell between the United States government and the Cherokee which ended the Revolution, the United States lacked the military capacity to effectively enforce its will (it's rights as property owner) on the tribes.

Further, it should be noted that the Constitution treats the tribes as their own sovereign political entities. This is why the term Indian, for purposes of the law, is a political classification rather than a racial or ethnic classification. This is also why Congress is typically granted near-unlimited (and sometimes extra-constitutional) powers in regards to the tribes under the Indian commerce clause.

One of the many compromises that went into creating the Constitution concerned the ceding of western lands claimed by the states (often up to the Mississippi River) to the federal government (to be used in the creation of new states) in exchange for a federal promise to remove tribes residing on lands within the current states.

Who owns the tribal lands, who has the right to purchase lands from the tribes, who has tribal authority to sell tribal lands, and whose law is supreme in tribal lands were all questions that came before the Supreme Court in 1820s and 1830s.

In Johnson v. M'Intosh in 1823, Chief Justice John Marshall used the discovery doctrine to create aboriginal title to try and answer some of these questions. In reality, the holding in Johnson is a mess (history almost certainly points to Marshall actually issuing this holding in preparation for another case concerning his own land interests in purchased tribal lands in the Yazoo land scandal), but it states that ownership of all land in the New World automatically transferred to the discovering European sovereign upon discovery.

Therefore, the tribes did not own any land outright. Period.

Instead, Marshall created a new property interest known as aboriginal title specifically for the tribes. Aboriginal title granted the tribes only the limited right of occupation, meaning they were allowed to live on the land, but it was not theirs to sell. This has, as you can imagine, had devastating consequences, and aboriginal title has been used in both Australia and New Zealand. See here.

So, the default rule for all tribal lands after 1823 is that they are owned by the United States government, but the tribes retain the right to live on their lands.

Finally, the President at this time is Andrew Jackson, avowed Indian fighter (or murderer) of the Seminole and Muskogee Creek in what was then Spanish Florida and all-around asshole in all matters regarding tribal sovereignty. In 1831, when the state of Georgia nullifies Cherokee law on Cherokee land and begins to physically seize the land, the Cherokee file for an injunction in the Supreme Court. This brings us to Cherokee Nation.

Cherokee Nation involved a claim brought by the Cherokee to enjoin the state of Georgia from enforcing Georgia law in Cherokee territory and, more importantly, stop the state from seizing its lands. Georgia wanted the Cherokee territory because the Cherokee had struck gold, but the questions of whose law held in Indian Territory (tribal, state, or federal) were also at stake.

In Cherokee Nation, Marshall held that the tribes are not foreign powers, but rather, domestic dependent nations. For immediate purposes of the case, this means that the Supreme Court lacked jurisdiction and was able to dismiss the claim, as a claim involving a State and a foreign power falls under the Supreme Court's original jurisdiction. Marshall would only manage to duck the question for a year, because…

… 1832 brings Worcester v. Georgia, and Marshall makes an attempt to correct course and help the tribes. In Worcester, the Court holds that Georgia law is null in Cherokee lands. He tweaks his definition of aboriginal title as well.

Aboriginal title now grants the tribe the right to sell their occupancy rights in their lands only to the monarch. Again, the United States as a successor to Great Britain in North America, gains this right. But now Marshall impresses upon the federal government a duty as guardian of the tribes to pay the tribes for this right. Worcester stood for (until this past summer and the Castro-Huerta decision) the bedrock principle of federal-tribal land ownership and jurisdiction:

Tribal lands are owned by the federal government. The tribes are allowed to reside on the land. State law had no effect within recognized tribal lands. If the federal government wanted to take land currently occupied by the tribes, it had to pay them for it.

It is a sort of legal fiction in a way: the United States owns the land, but because the tribes are deemed dependencies of the federal government, the United States owes a duty to pay the tribes for this right for any land cessions. The government is paying for the right to occupy the land in legal fact, but they are really paying for the land as if it is a land purchase. Again… it is confusing.

In any event, this enraged state governments. Congress had passed, and President Jackson signed into law, the Indian Removal Act in 1830. By refusing to enforce the Court's holding in Worcester, Jackson ensured that removal--the illegal force marching of most Cherokee, Choctaw, Muskogee Creek, Chickasaw, and Seminole tribal peoples to eastern Oklahoma--was carried out nonetheless.

In 1871, following U.S. expansion westward across the Plains, Congress declared that it will no longer make any treaties with the tribes. This comes about primarily due to constitutional duties in Congress. Treaty-making under the Constitution is left to the executive branch (President) and only requires approval by the Senate. However, the securing of monies to honor treaty obligations falls to the House of Representatives.

So the House has no say in treaty terms negotiated between the United States and the tribes, but it has the sole responsibility of providing the financing for said treaty obligations. The House gets tired of coming up with money for treaty obligations they have no say in negotiating, so they take their ball and go home. This is why there are no more congressional treaties with tribes after 1871. Instead, they will become Acts of Congress which require approval of both Houses or Executive Orders (which carry their own twisted legal reasonings when it comes to tribal land).

/u/Kelpie-Cat has linked the previous write up I did on Indigenous sovereignty under international law, in addition to their answer about the concept of property ownership. These two tackle a good bit of your question. /u/ExileInExile has also provided a good explanation that touches on the Marshall Trilogy of Supreme Court cases and establishes the succinct answer to your question, that being the creation of property law and that treaties are legally construed as property rights.

When the 1871 Indian Appropriations Act was passed that ended the treaty-making era with Tribes, it is indeed the case that this was done by the House of Representatives to curb what they viewed as gross expenditures being made through treaty obligations that they had no official say in. Though this particular legislation did end the treaty-making process with Tribes, it specifically stipulated that all previously signed treaties (that had been ratified and not abrogated, of course) were still in effect. So even though this moment represented a major shift in how the federal government interacted with Tribes and thus conveyed the subjugated status of Tribes in a legal sense, there was still a premise for the U.S. to construe Indian Tribes as polities from time to time. This perception, though, was certainly tempered by the preference for legal positivism that dominated the theoretical landscape by the 20th Century. Indeed, this became all the more apparent with the Lone Wolf v. Hitchcock (1903) case.

In 1867, the Medicine Lodge Treaty with the Kiowa and Comanche was signed. Like a number of treaties being signed at this time, article 12 required a vote by 3/4 of all adult male Indians on the relevant reservation to cede any further lands within the establish boundaries secured by the treaty. By 1892, Congress had created an allotment agreement that was fully approved in 1900, opening up some 2 million acres of reservation lands for these Tribes to settlement by non-Indians. Lone Wolf, a Kiowa Indian, took this issue to court on behalf of the Kiowa, Comanche, and Apache (who were subsequently incorporated with the two former Tribes through another treaty signed around the same time). Specifically, Lone Wolf brought the charge that Congress had violated the Medicine Lodge Treaty of 1867. The question before the Supreme Court: can treaties between the United States and American Indian Tribes be broken unilaterally by Congress under its plenary power?

Unsurprisingly, the answer was a resounding: yes. Because of its supremacy, Congress has every right (or so it thinks) to abrogate an Indian treaty or parts of an Indian treaty even if it violates the treaty itself. However, this is not simply by the virtue the United States oppresses Tribes. There is more to it than that! As can be inferred from my previous answer, Indian treaties stand on the same footing as international treaties in U.S. law. This was the case in 1787, 1823, 1871, 1953, and still is for 2022. So the process of abrogating an Indian treaty, and thus the legal rationale for the authority to do so, are the same. Because the U.S. Constitution has given treaties the same status as federal statute, Congress has sole authority to invalidate a treaty or parts of a treaty simply by passing legislation despite the responsibility of negotiating treaties resting with the executive branch and the ratification procedure being relegated to the Senate; any subsequent change affecting a treaty or a treaty stipulation(s) is thus superseded by the statute which then becomes internal law for the United States. This is the case for any treaty, not just Indian treaties. When Lone Wolf was decided, it was essentially establishing that Indian treaties were to be treated the same as any other treaty and that Indian Tribes were indeed subject to the plenary power of Congress. There is a question of whether this is consistent with having good faith toward Indian Affairs, a principle based upon the Doctrine of Trust Responsibility and that is related to the canons of construction provided by /u/ExileInExile. This is a point in the Indians' favor because it means our treaties were not being disregarded due to their nature--just simply due to injustice!

When we look back upon the Marshall Trilogy of Supreme Court cases, what we must identify are the actual circumstances before Tribes in the wake of those decisions. Ultimately, what Marshall decided for Tribes between all three cases can be boiled down to two essential restrictions on Indian sovereignty: the conveyance of land and the ability to deal with foreign powers (Canby, 2020, p. 83). Worcester was and is sufficient enough to demonstrate that the federal government, despite its assimilationist, oppressive, and paternalistic disposition toward Tribes, saw Tribes as sovereign and this interpretation carried through the end of treaty-making in 1871. As far as the views on property are concerned, I'd reckon to say that if Indians were able to convey their thoughts about land theft in court, then the cultural differences in this regard were moot. Tribes understood by 1903 that these documents we call treaties are what were used to secure land cessions from them even if only one side really considered them valid in a total sense. But by the 20th Century, Tribes had lost the political and military advantages they once had that could balance out the scales for treaty negotiations. Indeed, by 1900 the population of all Tribes collectively was approximately 250,000. Contentions over land disputes since signing treaties was basically par the course and it is the reason behind the creation of the canons on construction. The dominance of English, the preference for written documents, and the growing hegemony of colonizing powers all converged to ensure that Tribal methods of communication and cultural notions of land ownership were at odds with the growing world that sought to dispossess Tribes of their lands, methods and notions that ultimately did not matter to the U.S. who was only worried about using treaties and Western notions of ownership to secure a legitimate claim that both satisfied their own machinations and that they could bring to the world stage lest they be questioned by the Family of Nations who could then submit competing claims to other world powers.

Did this mean that Tribal notions of ownership or even the manufactured property rights they now possessed amounted to nothing? The best way to answer this question is to look at the 20th Century during the period when some would say Indian rights amounted to little more than a fairy tale. There are two points in particular. Starting with the latter one, it comes from the Supreme Court case Menominee Tribe v. United States (1968). In this case, the court ruled that the Menominee Tribe, though having had its relationship with the federal government "terminated" by an Act of Congress passed in 1954 (coming into force in 1962), retained their treaty rights for hunting and fishing established by an 1854 treaty. Because Congress had not made an unambiguous statement regarding the abrogation of the treaty rights, the court was inclined to rule in favor of the Menominee lest the federal government create a cause for a claim of compensation under the 5th Amendment. This is where we really build the argument that treaty rights are property rights and these are conveyed to the Tribe regardless of how they might've understood them at the time.

The former point was already in existence before 1968. Established in 1946 under the Indian Claims Commission Act, the federal government created a new court that would hear claims brought by Indian Tribes to recover damages from broken treaty obligations committed by the United States. The general process was that Tribes were granted a five-year period (1946-1951) to file a claim with this new Indian Claims Commission (ICC) and “after all appeals are exhausted, Congress appropriates any funds awarded to the tribe” (Pevar, 2012, p. 324). The ICC was abolished in 1978 by Congress, but the last claim was not finally resolved until 2006. Prior to this, Indian claims were authorized to be heard by the Federal Court of Claims in 1881, but it soon became apparent that this was ineffective because of the sheer number of claims and the difficult process of getting the claims heard in the first place (Oklahoma State University has kindly digitized the entire 43 volume set of decisions). This means that even before the ICC was created, the federal government continued to recognize the validity of these treaties despite their disregard for Tribal sovereignty overall. Of course, there are many complaints to make about the ICC, namely the awarding of strictly monetary funds rather than retro-ceding land titles and the extinguishing of remaining land claims once compensation was made. But the point here is that even though Tribal Nations might have held differences regarding land ownership, by the 20th Century, enforcing these notions wasn't a reality. The United States recognizes this reality and goes so far as to recognize the injustice endured by Tribes, but the entirety of the Doctrine of Trust Responsibility--the doctrine that says the U.S. has an obligation to protect and support Tribes--rests on the signing of these treaties. And because the U.S. wants to hold itself to its own Constitution (reasonably so, one would suppose), the treaties remain in effect regardless of any malintent and continue to be one of the few ways Tribes can address infringements on our sovereignty.

Edit: A word.

References

Canby, W. C. (2020). American Indian law in a nutshell (7th ed.). West Academic Publishing.

Pevar, S. L. (2012). The rights of Indians and tribes (4th ed.). Oxford University Press.