Post-apocalyptic sounds right to me, since the Pope said the Tower is "a remnant of an ancient yet advanced civilization" in ch. 2.
I more meant though, post-apoc from
our civ or not, which is less clear. I don't think we've seen anything conclusive on that front, no artifacts at all that are clearly modern let alone futuristic beyond of course the towers themselves. The "ruins of the past" the Mirror ramas had her dungeon in still looked medieval or at least 1700s or something, all stone.
Though the Kings speak of "Administrative rights" to the tower, like it's an advanced computer system. They talk as if educated in the present time, Pope understands space and orbital dynamics etc. But at any rate the author is playing things very close to his chest for now.
BTW, since you mentioned world building details, there was one more thing I noticed: the Mirror ramus says her new power after the flowering is too much to control with a normal human body. Well, the Pope seems to have no trouble controlling it.
Also, the Garland, who also has a flower, seems to have a burnt(?) face. At first I thought maybe she was abused by the Empire or something, but it could also be a mark of her using her power and her body not being able to control it.
Yep, the Kings are clearly something more than human. The Galia king seemed like he'd just evaporated from his clothing, perhaps their existence is tied to admin control over the towers. We've seen the pope wearing multiple faces but the face he wore on his last meeting with Galia king was kept hidden, maybe that was his original?
Anyway, such a cool setting, but so much implied or shown without any further explanation, like what's up with the rest of the world? This entire struggle seems to be in a small section of Europe, Papacy seems in the area of Rome, Empire maybe around London? Guess we'll see.