Succession was contradicted on release - It was explicitly set after Discovery returned to the Prime Universe, but Mirror Owo is part of the Shenzhou crew in it, while she was part of the Emperor’s honor guard and killed in “What’s Past Is Prologue.”
There's actually a canonical precedent for a character seemingly-vaporized onscreen later suddenly returning with no explanation whatsoever --
Lt. Galloway, who appeared in quite a few TOS episodes, but was phaser-disintegrated by Captain Tracey in "The Omega Glory," but who then abruptly returned in "Turnabout Intruder" (with his onscreen-credit being spelled "Lt.
Galoway").
So I simply chalk the whole "Mirror Owosekun"-situation up to maybe an identical twin sister or something else...if onscreen canon can get away with it, heck, I'm cool with it here too.
Succession also treated Airiam as an alien, which last season showed was not the case, and she’s in Terra Firma, part of the Discovery crew, alive and not cyborgified.
Not quite, re: the comics -- last night I re-read the IDW series after watching the episode, and Mirror Airiam is indeed part-human just like in the Prime Universe, but she waxes rhapsodic at a couple of points about feeling "not fully Human" and accepted by her Terran Universe crewmates (it's also mentioned that she has Human DNA):
There's the implication that Mirror Airiam has been a cyborg for much longer than her Prime-counterpart, although this can certainly be accounted for as differences between quantum-timelines, in terms of events.
Also, it seems that there's still some question as to whether that was actually a human Mirror Airiam in the new episode or not -- on Memory Alpha, the actress isn't credited in the role as playing the "mirror" counterpart of her character (unlike her other bridge-crew colleagues), and it might have been a different character entirely (or else next week we'll finally get confirmation that it was indeed fully-human Mirror Airiam).