Taylor is a teenager. Teenagers have moments of Drama and No One Understands Me and perceive the rest of the world and people in it(particularly their parents) through a lens that is completely unconnected to reality and the real state of events whatsoever.
I gotta agree with Stormseed, the stereotypical teenage!drama was overdone. Honestly, most of this chapter seemed like her reactions were chosen based on what would cause more drama rather than what would be in character for her. Pointless drama like this is one of the things that irritates me the most on stories.
And if you are going to make Taylor not spam her precog in order to keep the story interesting, make something happen in story
that explains it, like her using it to see how a conversation will go, saying something different in response to what she saw, and it make things go worse. As it is, you have her actually thinking about how she never uses it when it matters, and it just seems like she is constantly juggling the idiot ball.
Coil is best served, I think, in the background. We'll likely get something with him in the future, but I want to avoid having him too prominent because that wrecks him as an interesting antagonist. He won't make his move until he has things laid out exactly as he wants, if he makes a move at all. You thought it was the PRT, but it was really me, Coil, all along!
Taylor = teenager. Everything is drama.
And Armsy is just a huge bundle of optimism!
Honestly, I'd really rather you not have Coil be a major antagonist at all. You are already doing an openly AU story, so you could make things a little different. Coil is the main antagonist of almost every Worm story out there, for once I'd like to see a story where he isn't a Big Bad for Taylor to fight against (and no, curbstomp fics don't count).
When Taylor and Vicky landed on top of Coil's building as a "safe" place to talk, I groaned, in no small part due to the fact that, as both can fly easily and enjoy doing so, they could have a conversation guaranteed to be private by just staying up in the air.
As is, this feels like a story I read where they figured out Coil is using his power because they did something that doesn't make sense fire them (I.e. they were manipulated by his power to do it). This is not even close to the way his power works, but with how unlikely it is for Taylor and Vicky to have just happened to have landed on Coil's so he could find out about her. And yes, I know you said there might not have been cameras, but if that is the case than you are just bring a massive troll. That is your prerogative to do so, but it is likely to lose you some readers.