I don't have the time or will to watch a two-and-a-half-hour YouTube video, but addressing your specific assertions that you attribute to the video:

That the atomic bombings had little impact on the internal debates within the Japanese leadership over surrender.

This is the argument of many historians, notably Tsuyoshi Hasegawa, who argues that there is not much contemporary evidence that the bombs had a major impact on the surrender discussions. Instead he argues that the evidence of the Soviet declaration of war is much higher. There are other historians who dispute this, mostly relying on postwar recollections. Either way, it is very hard to tell which of these things had a greater influence, or whether there were influences that were unsaid. But in general, I would say that most historians of the bomb these days accept that the bombs at most may have contributed to the final surrender decisions, but were not in any way the only influence on them.

That the atomic bombings were not done to avoid an invasion, and an invasion was never seriously considered.

The first part is correct (the bombings were not done as an alternative to an invasion), but the latter is not correct. There were serious invasion plans already in motion. The land invasion of Kyushu was scheduled to begin on November 1, 1945. This was a serious plan that was already authorized by the President. The plan to invade Honshu, which would have begun in early 1946, had not been authorized yet, however — it was a "wait and see" proposition.

It is not entirely clear that, by the end of the Potsdam Conference, that Truman et al. thought the invasion was likely to happen, both because of the atomic bomb and because of the impending Soviet entrance to the war. But the plans were still on and they were serious.

Again, however, the use of the bomb was never framed as avoiding an invasion. The plan was to bomb and invade, and perhaps even use atomic bombs in the service of an invasion. It was not at all clear that the use of one or two atomic bombs would actually end the war.

That the American leadership were aware of the dire situation in Japan, and the inevitability of its surrender.

They were certainly aware of the dire situation in Japan, and that the Japanese leadership was divided on how to deal with it. I think the way I would phrase it is that they were aware of the inevitability of Japanese defeat. But defeat is not the same thing as surrender, much less unconditional surrender. There was no question that Japan was going to lose the war. The question was, when, and on what terms?

And that ultimately the bombings had little impact on accelerating an end to the war, and that they were largely used for political purposes more than for military necessity.

Again, the role of the bombings on Japan's decision to surrender is controversial. But I think what you are really getting at here is the intention in using them. In looking at the various people who were in charge of the use of the bombs, and who weighed in on the planning, one sees a variety of motivations. Most of them were along the lines of, "we have a new weapon that might contribute to the end of the war, and we are thus obligated to use it." That is what I would call a military purpose, although it is also a question of political obligation.

There were also other motivations, sometimes held by people who also believed the above. One of these, which was best articulated by James Byrnes, the Secretary of State, was that the use of the bomb would give the US an edge over the Soviet Union in the postwar. This is what is frequently invoked as a "political" motivation. It is plainly evident that Byrnes felt this was an added benefit for the use of the bomb. It is not clear that this was his only motivation (people can have more than one) nor that this was the sole motivation for the US using the bomb. There is much evidence that this was not the main motivator for most of those involved.

Another motivation, and one that I have found most commonly among the scientists involved in the planning, was that the public debut of nuclear weapons needed to be sufficiently horrific that the world would pledge to not use them in war again and perhaps avoid an arms race. This is a very different sort of "political" motivation.

Anyway — I am engaging here only with your bullet points, not the video itself. So I am not really commenting on the video, which I have not watched (and do not plan to). The video sounds like it is heavily indebted to accounts like that of Tsuyoshi Hasegawa's, which is fine (though I always prefer to highlight that these are particular interpretations, and there are other interpretations as well), with perhaps some of Gar Alperovitz thrown in (the "scare the Soviets stuff"), which is less reliable if taken too far.

In many of these things, there is considerable room for historical interpretation and disagreement. History is not a static collection of facts, especially when one is looking at something as complex as the end of the Second World War, where you are really asking about the subjective views of a number of very different people in different countries. This is one of the reasons it is very hard to present "sufficiently," in the sense of giving the reader or listener a sense of what is known (some things are definitely known) and what is an interpretation, and where those interpretations come from and what evidence they are based on. Videos in particular make for a difficult presentation because the citing of evidence is always difficult in a visual media. This does not make them bad, but it does make them at best a starting point for thinking about these things.

Hasegawa's Racing the Enemy is the source I usually recommend people start with if they want to go down this path more deeply, because it covers a lot of ground very nicely and professionally, even if one does not agree with his ultimate interpretations.