Okay I just remembered this blog TSSL showed me way back (thanks again @TSSL 
) that had some good introductory stuff on crafting plausible matriarchies that move away from the lesbian amazons who seem to do very little but cater to the gaze of the straight male audience.
Since you said homo Atlanticus is technically its own human offshoot, who unlike the Neanderthals survived mostly intact to compete with modern homo sapiens I wonder if there is a subtle difference in biology beyond the eye cones, more specifically in the female reproductive system.
Warning, some world-building 101 questions, rambling and wild speculation ahead
From the mythcreants blog:
“Even better, you could make women infertile when they are under stress. That would make it very difficult for a man to get a woman to have his child under duress. Whatever your methods, your goal is to make pleasing women the only way that men can reproduce. That will change the balance of power dramatically.”
Though of course that biological change alone is not sufficient the create a matriarchy even if it does increase female power and gender equality somewhat. It does have me wondering if ancient Atlantis during “the reign of kings” was already a matrilineal patriarchy. Which is not as far-fetched as it sounds as before dna testing and even now matrilineal is actually the more efficient way to determine lineage.
However while an important biological advantage it is not itself enough to prevent patriarchy although it would shift men’s tactics more towards being peacocks and casanova’s rather than brutish thugs.
Although a matrilineal and probably matrilocal system in ancient Atlantis even when men were in control of the bigger share of cultural and political power would likely still have meant that even back then Atlantean women had at least somewhat more influence and opportunity compared to many other ancient cultures which would have left them in a better position to seize the reins in the immediate aftermath of the traumatic cataclysm.
One point of minor contention I do have with the mythcreants is the meat and vegeterianism thing as in adulthood and adolescence women and girls would actually benefit more from the protein and iron in meat than boys do, comparatively. Even if in many if not most of our cultures the lion’s share of good meat historically went to the guys. This would probably have held less true for pre-cataclysm Atlantis and likely not at all for the post-cataclysm and modern one. This has the beneficial side-effects of eliminating the iron-deficiency and anemia that still plagues too many modern girls and women and particularly over generations would tend to make women larger and stronger and thus narrow (though not completely eliminate) the strength gap between them and the boys.
Of course if you really like vegetarianism I suppose you could hand-wave in an Atlantean staple food that is (unusually) high in protein and iron for a plant. 
It does nothing for the relative expendability of men and women although I think it may be assumed that even if the common Atlantean grunt soldier is still male some of the more elite ones and a majority of the officers are women.
The last side effect is that it would change the beauty standards too and likely make having (some) visible muscle and weight a female beauty standard in Atlantis.
But then beauty standards tend to be less stringent and less of a concern for the dominant gender anyway.
We of course already know the male beauty standards of Atlantis are much closer to Japan and Korea than the West, though that is mostly aesthetic as those K-pop idols can often punch just as hard or harder than the grizzled heroes our Western cultures tend to lionise.
It is another thing that heavily points to Atlantean men operating more like peacocks when it comes to dating and sex.
I also wonder with those beauty standards if Atlantis ever does open up more if it will be Atlantean instead of Korean idol groups taking the world by storm, particularly if Korea too is still in the thrall of a much more conservative Joseon Kingdom, whether genuinely independent or a vassal of either Japan or China still .
I have many more questions on the lore but the more contemporary ones will probably be revealed through gameplay later on. So for now I’ve restricted myself to some speculations on pre-cataclysm Atlantis and further possible biological differences present in homo Atlanticus as a species.
Nah, the Roman Empire ain’t around anymore, but the British Empire still hangs on and depending on whether or not they still have India and let the tail wag the dog a bit they might be the foremost great power, aside from the evil empire of Atlantis itself. Italy may or may not still be a monarchy tho. Like in Kaiserreich it seems (constitutional) monarchies are much more prevalent in this world and of course Japan and maybe even Brazil might still be empires in name and even the Kaiserreich itself and the Romanov dynasty in Russia still seem to be around. The upside would be that I can’t possibly see a Brazilian emperor being worse than Bolsonaro.
I guess republics are in the minority in this world, obviously the USA is one and it is likely that France is one too and there are likely a relative handful around in other places too.
We’ll probably have bodyguards of some sort, though to my mc they feel more like prison guards and at some point, if the game allows it, he’ll at least try to ditch them to explore Atlantis on his own and actually meet some of its ordinary people.
