I recall several What If. and Dark Knights where they did this. Supers as knights in medieval times and Superman landing in Germany instead of America.
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I feel like the Marvel and DC takes on this kind of thing have been really, really bad and frankly lazy examples of what you could do here, because pretty much all of them relentlessly and I do mean utterly relentlessly focus on making the heroes/villains very similar to what they are in the main setting, immediately aesthetically recognisable, immediately having the same approximate mindset, using their powers in a similar way, and so on.
And I don't think any of that makes sense at all, and frankly to me, it's not even interesting. I want to see the difference, not fate's inevitability.
I do think people often do a slightly better job with Superman than other heroes, oddly enough, because even comics writers who fail to engage brain much tend to realize how much the Kents and Smallville influenced Superman, and how if he has different parents and environs, he's different, whereas the opposite seems to the case for I dunno, literally every single other hero they do this with, where they're like, 95% similar but with some twist like they're in the Yakuza or something.
But what about supers first appearing in Warring States Japan? Or the Crusades? Or in the cyberpunk future?
I think the key thing will be like, what's the power source?
Because, y'know, cyberpunk future, tons and tons of people are on "low-end superhero" (and some mid-end!) in terms of powers. Like, Adam Smasher or David Martinez could probably take out half the X-Men, even facing multiple ones at once.
So we kinda know what merely possessing cybernetic superhuman ability looks like there.
But if you suddenly had, say, X-Men-style mutations emerge, absolutely all hell would break loose in a cyberpunk setting, as every megacorp on the planet tried to either gain control of mutants, replicate the powers (and commodify them), or the like. Whereas if you had a good-natured wildly superhuman alien or ten arrive, they might just absolutely smash the megacorps for being evil, or might
try and do that and end up causing some kind of apocalyptic destruction as the megacorps unleashed absolutely every terror weapon and secret project they had brewing to try and stop them. I feel like in a cyberpunk situation, people trying to mind-control superhumans in various ways is likely to be a major factor, either by like brute force cybernetics attached to override them, drugs and VR to "reprogram" them, nanites to alter their brain/body chemistry, brain bombs (the ol' Suicide Squad) or whatever.
In the Crusades I think it'd probably start off with everyone saying "Our god did it!", but literally within 50 years, the most powerful surviving superheroes would be taking a more "I AM GOD, ACTUALLY!" attitude, and have cults dedicated to them, personally, and probably a whole bunch of other superhumans who were weaker than them serving them. Christianity and Islam would probably kinda be sidelined or even basically robbed for iconography and ideas, and then kicked in a ditch. Strange cults absolutely flourished in the middle age, and when the Catholic church can't really tell Templar-man "Actually you're a heretic and excommunicated" because he'll just fly to Rome and glower threateningly at the Pope until the Pope says "Sorry, actually you're fine, he's a papal bull saying you're fine and a living saint and your followers are spot on", it's only going to happen more.
First-mover and second-mover advantage would also be huge in the crusaders, because if the Catholic church did manage to get a loyal "heretic killer" squad assembled quickly enough they might be able to lock down all the inevitable "Hmmm kinda feels like I might be Jesus 2.0" people.
If the empowerment was also equally common for both/all genders, that would really mess with the dynamics of the medieval world, because, if fully 50% of the most powerful people on the planet, people who can vapourize your stupid column of knights and push over your castle are women, uhhhh, I don't think they're going to appreciate you treating women really badly. It's not like people didn't have feminist ideas in the middle ages. They sure as hell did, it kept coming up, over and over. It's just they tended to be y'know, brutally repressed or hidden away. But I think being extremely powerful would rapidly change that. You might well find gendered conflicts between superheroes too. Also, good luck telling Templar-man that being gay is a terrible sin when he has decided he wants to marry his male fiance, Mr Pope. I don't think it would be "all good" - there'd probably be some superpowered genocides and so on.
I do think "knightly virtues" might come up, especially if a lot of heroes were around a similar power level - it might well act as a sort of détente to have most supers (across religions and cults) agree to a somewhat-fake but also kinda real "We kill peasants, not each other" deal.
Anyway, that's enough for now - I think you could really do a lot with these and others.