I'm not sure TBG has the same variety of species in 2300 that even the movies had, but possible.
Like I said """is""". I assume that events and places and things from canon exsist
somewhere unless specified otherwise. We just don't... mention it. It's easier to keep track of that way. (I mean, not that the Shitty EU is in any way better, it is worse in many ways. The sense of scale is so wonky and shifts constantly)
On Earth population: The (noncanon) ST: Star Charts book listed the 2370 Earth census as 4.2 billion people. In First Contact, the fully-borgified future Earth had 9 billion drones.
One would expect the real number to be somewhere between the two. We also never get numbers for aliens in that.
By TOS canon, 37 million died in WWIII. By TNG canon, that number was 600 million (with about 30 million dying to the Eugenics Wars in specific).
By EU canon, Mars, which we can expect is the largest and most developed human colony, is about 130 million strong.
In all likelihood, the majority of humanity is still there on Earth right now, I think.
(Also α Cen has like 21 billion in the EU but this is due to the EU placing another species of UFP members there)
I've figured that the low death statistics for WWIII are mainly due to that listing only the "Direct" deaths of the Bombs and leaving out starvation, disease (some of it genetically engineered to really drive home the "Genetic Engineering is bad" thing), and natural disasters.
I also expect that half the human race is scattered out in penny packets of hundreds of those 10,000 to 10 million colonies scattered around (Some settled by sleeper ships botany bay style maybe hundreds of years away.) We just don't hear about it because we only "see" systems Relevant and important to Starfleet (And that Oneiros can whip up an extra colony whenever he needs to)
And the Canon number of "9 Billion drones" seems light in a universe where the Dominion was going to kill 900 billion before the war's end.
Like Earth's alien population is probably fairly large due to slow accretion. During the time of Enterprise, before the foundation of the Federation, you probably had at most a few million merchants, diplomats, and specialists brought in to help bring Sol's industries up to standards. Any many of those probably had families and stayed.
Then over time diplomats and other folk like that come and go, and some stay.
And then you get the opportunists, hangers on, and idealists, those drawn to the fact that this is the Federation's capital. The Andoiran woman that emigrated to Earth to work with the Galactic Rights Commission and brought her large family with her. The Tellarite workers who came to help align Utopia Planetia with federation standards and are still here because they understand and built the systems. Lobbyists from the Orion Retail Commission trying to crack into Federation markets, with literally hundreds of thousands of Orion workers in Sol trying to convince Humans to buy their stuff. Yrillian refugees from the last big civil dust up wanting a different life. All the Starfleet aliens that retired from Starfleet but live on Earth as consultants.
It's just slowly built up over time. And the native Human population is probably relatively stable due to being a First World equivalent (Zeroth World? Negative-First World? ... Successful Second World? > : P) so all the humans leaving to tip Colonia Prime from eight to ten million or whatever slowly deplete Sol's Human population without replenishing it with humans. But no one notices that because official 2300 census tallies are 25% higher than they were in 2200.
I actually wonder if Trek Humans actually have this sort of culturally prominent Inferiority complex that we don't recognize because no one looks for it? All those high achieving Starfleet officers and over representation in Starfleet flag ranks is not because Humans inexplicably have all the power in the Federation, but because they feel they have none, so they make a massive effort to perform and overachieve. All the random colonies are part of this too, an almost subconscious desire to show the rest of the Galaxy that Humans can hang with the big boys. Sure that Vulcan of Three Million has been that way for a century; but a century ago but the next door Human colony of four million didn't even exist!
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I also wonder if there is a decently large diaspora community in the Orion Union? They are a nearby polity where a lot of the ideologies and economic ideas of today (Which are not present
at all in Trek Humans) still exist and are near deified. A lot of people angry with the "New Economy" probably also had a diaspora, but not to colonies, but to existing societies.(And freed slaves...)
Also: my headcannon is that there is also decently large Orion community of "Terraboos". Human cyberpunk is especially well regarded, though fantasy (read Star Wars and other space opera) is also well liked. As well Orion Pizza is well regarded as just about the best in the galaxy. Much as the Klingons stole Shakespear, the Orions stole Pizza!
