I disagree with what you say Civ allows you to do. To me Civ does not allow me to see what would happen if the Aztec became the dominant power in the world, without morphing into a later real-world super power. Aztec in the modern era are analogous to any -Western- super power of the same era. Aside from the music and unique buildings, there is nothing in Civ that really makes the Civilization you are playing set its own course. They all, always, end up in the same corner: our current, western world. It's actually quite sad in my opinion.
That's overanalysing - the units and options in Civ games (other than the Strategic Defence Initiative, Giant Death Robot, X-COM Squads and Civ VI's entire Future era) are all things that existed in the real world. Since the Aztecs never did develop modern technologies there aren't any modern Aztec units they could have drawn from. The point is not that Civ represents a plausible alternate history, it's that people are playing as what they think of as the Aztecs (because that's what the game calls them and they have stereotyped 'Aztec' abilities) and leading them to a greatness they never had in reality. Most players aren't going to look any deeper than that.
Democracy in the modern times, because the USA adopted it then (nevermind the pure democracy in Greece, or tribal democracy).
Republic/Classical Republic has always been Civ's take on classical systems (and resulted in voting in those versions of Civ that had that mechanic) - yes, it combines everything from that era into an abstraction, but then 'Democracy' groups modern US Republican systems and British-derived Parliamentary democracy into a single system, since while the distinction is largely neglected in modern discussions of 'democracy' the two systems have different origins (the US system as a deliberately novel political framework based on a combination of existing British-inherited institutions and a conscious revival of classical democratic concepts; the British one as a gradual evolution, ultimately from a system of tribal councils and advisors to the ruler) and function differently to this day. Even in this post you refer to the modern democracy as "American" even though parliamentary democracy is not only both older and the dominant form in most of the world, it's the one the Americans themselves implement in countries where they've encouraged or in some cases actively enforced democratic transitions.
Yet FXS has always made games where history progresses literally as it did in our times, the only difference is that the timing might be different, and the name of the Civ leading the world, might be different. Of course, the world build is different on random maps, and war-outcomes, but it always is tech A before tech B, Civic A before civic B, because for us it happened that way, and therefore it's the only logical conclusion. We started reforesting in the industrial era, so that's how it goes. No, there is evidence that that happened waaaaaay before in the Amazon.
And in the Congo, but not as a planned activity, simply as regrowth following abandonment of settlements in the area. As for technological progression, in modern Civ games the primary driver is the need of game mechanics and the actual tech tree has long since ceased to reflect a reasonable real-world technological progression - Civ V in particular had notorious examples like nuclear submarines without Nuclear Fission, and I think Robotics without Computers.
I want Civs that start out as slave-owners and have not made the morality jump, or do so because other civs in the game do so too (not because a unit gets upgraded). I want Civs that don't know the concept of slave ownership and are completely pacifistic like the Moriori, and carry this on throughout the ages, or learn to fight because other civs dictate them.
I'd just like slavery to be acknowledged as a mechanic and not treated either as a 'Hollywood pharaohs whipping Pyramid builders' production boost or applying the notion that the industrialised slavery of the colonial era and the use of slaves principally for agricultural production in plantations is the same phenomenon as classical slavery. As with 'democracy' the particular American outlook of dominant game and media producers tends to treat often loosely-related phenomena as the same thing, and the American experience means that the lens through which 'slavery' is understood tends to be that of the African slave trade, although in a historical context this is atypical of slavery systems more broadly.
This may be asking for too much, but I've always thought it would really be great if the tech and civic trees were individualized for each player and each game, morphing somewhat based on the path you take and the choices you make. I realize that might be difficult to implement, and yet imagine how much more true to life it would be, not to mention making repeated game plays more enjoyable.
The fact that you get to actively pick and choose which cultural traits you want at specific points in Humankind seems to be a source of dissatisfaction (whether you give them immersion-breaking names or not). A lot of people who've wanted this sort of progression have wanted some way for your civ to 'naturally' adapt to its surroundings.
For instance, settling a specific landscape might open tech options - so that instead of saying "Ah, I'm on the coast. Guess I'll be Phoenician this week", you may not be able to access coastal techs unless you are on the coast - but will be incentivised to do so if you are. You could get rid of the oddity of being able to research iron working without ever seeing any iron. You may need a certain extent of nearby forest - and possibly nearby deep water - to be able to develop Renaissance-era and later ships.
Contact with civs that have other technologies or cultural achievements may increase your access to those - not in terms of tech trading, but possibly you could passively develop knowledge of techs a neighbour has, and the rate of that acquisition could increase with trade or cultural exchange (if there's a system for monitoring relative cultural influence, such as migration). Contact with nearby civs that have similar tech might unlock options for more advanced techs of the same type, and war may increase access to and progress towards military technologies - for example, technologies like gunpowder that were developed elsewhere reached greater sophistication in a European context where there were a larger number of states competing with one another to get an edge than they did in China where that selective pressure didn't exist.
I'd say Endless Legends/Endless Space style heroes is exactly what we're looking at.
Sadly, I suspect this is the case. I don't like hero systems in general, but Amplitude's games revolve so heavily around them that I'd be surprised if they're absent.
Hopefully Amplitude does not perpetuate Firaxis' strange obsession with Sejong's science. Korea became a science powerhouse in the 90s, which is no doubt why Firaxis focused in on Sejong's academies, but I wouldn't say that a focus on science has been characteristic of the bulk of Korea's history. Since Amplitude is clearly not considering themselves bound by Firaxis' traditions, I'm hoping Amplitude will instead focus on Korea's religious and cultural history (Goryeo ware, anyone?).
On the other hand, we've seen that Humankind's Babylon has a science icon, even though Babylon was not at its most notable as a scientific powerhouse. I suspect Civ has such a pervasive influence on players' expectations within this genre that we'll see a lot of the more consistent Civ themes carried over to Humankind.