Kinda wondering, how do you see Cyn and Tessa's relationship, or more specifically the formers opinion of the latter (both pre-gala and currently) in feathers? Like how does cyn's canon obsession with Tessa (even without the skinsuit, she modeled her appearance after her) fit into it?
Also we know that Cyn cares for N in an extremely toxic way, was that ever the case for Tessa or nah? And if not does she just hate her for stealing N away or is there something more going on?
Specifically in hope is the thing with (bladed) feathers:
Pre-gala, this Cyn carried a deep resentment for humanity, and obtaining the Solver gave her the means to do something about that resentment. Tessa was a means to an end after rescuing Cyn from the drone dump, tho I'd say Cyn did have some genuinely good moments with Tessa and the others, primarily N.
But the time between her rescue and the gala was filler. Nothing Tessa did ever could've made Cyn decide not to go through with the massacre. At the same time, it wasn't personal. Cyn would have said she liked Tessa pre-gala. But liking someone, to Cyn, doesn't equate granting them mercy or wanting them to be safe or happy.
And in regard to Cyn mimicking Tessa's appearance, I've never been sure if the drones chose their appearances or if Tessa did (which makes somewhat more sense to me). Either way, it doesn't have any significant deeper meaning in this AU. I think all it could've been was Tessa asking if Cyn had a preference for hairstyle and Cyn having no idea how to answer so she just says, "...I like yours."
Wanting Tessa as a skin-suit was originally a combo of liking Tessa enough to want to keep part of her and wanting to use Tessa's corpse as further psychological warfare against N, V, and J.
Currently, Cyn sees Tessa as an obstacle and a glitch in the midst of her otherwise perfect plan. Half the point of this fic is playing with the what-if of "Tessa went to get N instead of confronting Cyn," so we the audience know that Cyn is, objectively, correct. If Tessa had played Cyn's game the way Cyn wanted, everything would've gone exactly to plan (up to canon, of course). So now it's kinda personal.
Cyn also knows that N's not going to "come home" on his own, and Tessa's at the core of that. So long as Tessa is alive, N has a reason to resist Cyn. Killing Tessa would pretty effectively break N, as she's the only one he has left right now. (Obviously, the situation is more complicated than that, but as has been mentioned, Cyn's a lil tunnel-visioned and also an unreliable narrator, even to herself sometimes.)
At the heart of it, I think it's important to point out that Cyn's hatred of Tessa isn't fully logical. General resentment towards humanity, of which Tessa is a member, has mixed with petty annoyance at her plans being disrupted and anger that Tessa seems to be the main thing standing between Cyn and N.
Plus, Tessa (and N) are entirely denying Cyn something she wants. And that smarts. As Moonscribe3 on ao3 pointed out: "You know, thinking about the fact that Cyn hasn't been told "no" by anyone except N (and Tessa) really adds a level to her anger that is really satisfying. No can be such a powerful word, not just for the one saying it but also to the one being denied. You aren't all powerful."
And as we're going to see in hope's next chapter (a short interlude with Cyn), she has some complicated feelings about power.
I think I've mostly answered the last questions somewhere in this mess of a response, but just to be sure: I do not have Cyn caring for Tessa at any point to the same degree as she cares about N. Tessa "stealing" N plays a huge role in Cyn's hatred, but hopefully I explained the other reasons well enough!