Part I

So the first thing I feel like I need to address here is how extremely exaggerated Achaemenid egalitarianism is. It's not that the various subject peoples weren't relatively equal, but that this was not unique. In general, ancient Near Eastern Empires were happy to let their subjects speak whatever language, wear whatever styles, and worship whatever gods they wanted. The Hellenistic Greek and Roman efforts to acculturate their whole empire was innovative. Possibly the most egregious topic that comes up on the subject of Achaemenid generosity is slaver, which they definitely practiced and did not abolish despite persistent internet rumor (discussed in this older thread).

That said, on to your actual question. Despite the disparate nature of internal Achaemenid sources, this is actually one of the few questions where they can be extremely helpful. Many royal inscriptions, especially from Darius the Great list the lands of the empire, which are also frequently identified as peoples of the empire, suggesting each "land" was roughly equivalent with an ethnic group. That's not really surprising. Most ancient peoples viewed land as the country of a given people. Like many ancient Near Eastern inscriptions, these are cataloged with a series of letters to indicate the "author," location, and which inscription at that location from that author if there are more than one. In chronological order, the major inscriptions with Achaemenid territory lists are: DB (The Behistun Inscription), DNa (Darius' Tomb), and XPh (The Daiva Inscription).

The major foreign source for the territories of the Achaemenid Empire is Herodotus' list of satrapies in Histories 3:89-97. As a foreigner, Herodotus' actual numbers are probably incorrect, and his numbered satrapies seem to be his own invention. However, his Greek perspective actually sheds some interesting light on the situation. The royal inscriptions describe the whole empire at a fairly macro-level, but Herodotus addresses some minor ethnic groups that do not qualify as their own "lands" in the inscription record. Additional information can be gleaned from Greco-Roman authors who mention smaller tribes or ethnic groups in their storytelling

Taken together, all of this is used to create lists like this Encyclopaedia Iranica article or Ian Mladjov's maps to identify different levels of satrapal administration, usually divided up around ethno-linguistic groups. Those resources will present a much more comprehensive list of all of the little local ethnic groups referenced by the Greeks than I will, mostly because they can generally be lumped into a larger and better attested ethno-linguistic category.

You asked for a comprehensive list, so here's comprehensive list of every major group From Greece to India and Kazakhstan to Sudan c. 500 BCE. Since none of the inscriptions are laid out in perfect geographic order, I'll just list them in my own order.

Persia, Elam/Susiana, Media, Parthia, Chorasmia, Sogdia, Bactria, Aria, Drangiana, Arachosia, and Gedrosia/Maka

These are the broadly Iranian group. As the ruling group of the empire, Persia was usually left out of the subject lists. Each individual satrapy roughly represents a major ethnic or cultural distinction of some sort. Within those standard groups Karmania, Hyrkania, and Margiana are often identified as their own distinct regions and peoples occasionally seen as part of Persia, Parthia, and Bactria respectively. They can also be divided into two major linguistic sub categories. The first four all spoke Western Iranian languages, closely related to Persian itself. The others spoke Eastern Iranian languages, a category that includes later recorded forms of Bactrian and Sogdian as well as Avestan (the liturgical language of Zoroastrianism).

Within this "Iranian" category there are two noteworthy outliers. Elam, the region around Susa, was home to the Elamites, whose culture and language predated Iranian presence in the region by millennia. The Elamite language is considered a language isolate with no related tongues by most linguists, but it was also the administrative language of the royal palaces and Elamite people and culture were still thriving in Persia as well. Despite what seems like a clear difference to modern scholarship, Darius' implies that he considered them Iranian (literally Aryan) in the Behistun Inscription. The other outlier is Maka, which applied to Gedrosia, roughly modern Balochistan, but possibly drew its name from the Oman promontory, which may have been briefly occupied during the early Achaemenid period. That part of Maka would naturally have been home to proto-Arab speakers or some otherwise unknown group at this time.

Looking east we have:

Gandara, Sattagydia, and India

These are the Indian group, though there was probably a significant amount of cross polination between the westernmost "Indian" area and the easternmost "Iranians," and actually I should note that we really don't know where or what Sattagydia refers to. It's name literally means "land of the hundred cows; it's usually lumped in with the other two in the royal inscriptions; and Sattagydians and Indians are depicted in similar costumes, so scholars make an assumption. This also includes areas that appear in the earliest Buddhist and Jain histories of this period.

These people would have spoken Indo-Aryan or Vedic language(s), including Sanskrit and the predecessors to most languages in modern Pakistan. Given the many cultural similarities between ancient Iran and ancient India, including their use of the word Aryan, and where these satrapies are usually placed in the royal inscriptions, it is possible that the Persians did not draw a distinction between "Indian" and "Iranian." They may have both been considered Aryan at the time.

Looking north we get into the territory of the Scythians/Saka:

Haoma-drinking Saka, Saka with pointed-caps, Saka across the sea, and the Dahae

This is at least how Darius and Xerxes described the different groups of steppe nomads they encountered. How much actual political power the Persians had on the far side of the Jaxartes/Syr Darya river is up for debate. Darius was able to install a king of his choosing for some pointed-cap Saka, but we know basically nothing about the actual political geography of the central steppe at this time.

What we do know is that any of these groups could have included a huge number of tribes, organized into different alliances and confederations, all with possible relationships to more specific groups like the Massagetai from Herodotus or the later Sarmatians. They were all broadly part of the Scytho-Siberian cultural continuum that stretched from southwestern Sibera to the Danube, and in this region they spoke another group of Iranian languages. They are usually listed apart from the other Iranian regions, but the Behistun Inscription does suggest that Darius acknowledged their Iranian-ness.

The Saka across the Sea and the Dahae present their own challenges for modern scholars. The Dahae first appear in XPh, but were later remembered as a powerful confederation that lived on the eastern shore of the Caspian Sea and eventually spawned the Parni tribe that went on to found the Parthian Empire. Since XPh doesn't mention Saka across the Sea, some speculate that the sea in question might be the Caspian and that Xerxes just used more specific terminology than his father. On the other hand, Saka across the Sea are listed with the European territory in DNa and other scholars think they refer to Darius' first European expedition, which actually failed according to Herodotus.

This also probably a good time to pause and address the question of equality again. In Herodotus' description of the wars in Greece, these are the primary groups that appear in the Persian army. If everything was equal, it would make much more sense for the Persians to lean heavily on the provinces closest to Greece to supply their troops, but this does not seem to be the case (on land at least). Instead, the Persian army that engaged the Greeks was largely composed of these eastern "Aryan" peoples, possibly suggesting some kind of ethnic preference by the Persians themselves.