The Federation were still operating warp drive ships (as were everybody else), and they were already in conflict with the Emerald Chain. Book makes it clear early on that there’s plenty of conflict in this chaotic era, and (if in a smaller scale) we see warp ships fight all the time. Starfleet is limited and isolated because they have so comparatively few ships left from the Burn, not because they won’t engage at all. Everybody may be worried about warp ships exploding again, but they’re still using them, more than a century later.
And overvaluing things from the past (in their enemy’s view — again, all we see is some old movies) isn’t the same as worshiping the ground it walks on… and a starship showing up from the past, in an era where that’s specifically illegal, of course isn’t going to be immediately welcomed. (Though in the long run, they’re obviously pretty happy with it.)
I’m also just going by what I saw onscreen (though both “Calypso” and the rest of DISCO — because that’s what we have to go on.
Please understand that I’m not trying to prove you wrong here — I have no stake in however they choose to resolve this, if they do at all. But just from what’s onscreen, there’s no reason to doubt V’Draysh and the Federation being one and the same—never mind Michael Chabon’s then-Word-of-God that the first term is a corruption of the second, or the dialogue in Season 3 where Minor Villain Whatshisname calls them the V’Draysh at least once.
(And of course, it could always turn out that was a different era after all, and the V’Draysh were big ol’ meanies then. I don’t expect that, but it could happen.)