i've got to disagree here, i think vi's arc in act 3 is incredibly well done. not just that but it's also necessary in order to finish her season 1 story, because it's what she's been waiting for since the night everything went up in flames: it's her chance at a do-over.
(i apologize in advance for the essay, y'all know how it goes lmao)
for vi, the end of episode 7 and the start of episode 8 are a subtle but pretty exact mirror of the end of episode 3. powder/jinx causes an explosion, harming someone vi cares for. vi gets emotionally overloaded and does the only thing she knows how to do when that happens: she separates herself from the situation (and i'll talk about this more in a minute). once she's gotten a second to breathe and start thinking clearly again, she tries to go back, but is prevented from doing so by arrival of enforcers. and both times, it's too late anyway, because silco has gotten to her sister first.
last time she got thrown behind bars and was helpless to stop what came next. but this time, she's free. she can do something.
the decision she makes defines her final arc of the season: she has to stop silco, no matter the cost, because it's the only way she'll have any chance to save her sister.
her realization here wasn't sudden, but instead happened one gradual step at a time. vi assumed that if her sister survived, she must be silco's prisoner, but sevika threw a wrench in that theory. "she's like his daughter." however, sevika isn't trustworthy, and vi doesn't really get a chance to process what she said anyway.
when vi reunites with jinx, things quickly spiral out of control and she catches her first glimpse of the person her sister has become, but her behavior is probably still easy to rationalize even if it's troubling. jinx was acting in self defense, or at least in mutual aggression. the blurred line between the two is something vi understands well from her time in prison.
then ekko, one of the only people left in the city who vi does trust, backs up what sevika had said. jinx is violent and dangerous because she wants to be. she works for silco because she wants to. vi seems to be able to see some truth in ekko's words yet she still pushes back, defending her sister.
but it's with these words in her head that vi sees the proof with her own eyes: jinx bombs the blockade, catching not just on-duty enforcers but also caitlyn and ekko in the blast. there was nothing even resembling self-defense here--it was simply an act of war, committed on silco's behalf.
and then, jinx opens fire on vi herself, and the truth can't really be denied anymore.
"all that's left is jinx, and she belongs to silco."
to be clear, when vi walks away here, i don't think she's thinking ahead, crafting a plan, or behaving rationally at all. she's hurt, she's scared. she thinks her sister just tried to kill her, and she's too overwhelmed to handle the situation so she walks away. it's a pattern she repeats throughout the season--in episode 3, here, then to caitlyn in the very next episode. and i'm not here to pretend like she's right to do it, in fact it's one of her most glaring weaknesses. but it's painfully in character, and not bad writing at all.
so full circle back to the start: once she's away from the source of her stress and has half a second to think, vi realizes what she has to do. if what ekko said is true and jinx belongs to silco, then silco is the problem. he has always been the problem, so she has to take him out of the picture. and, to her credit i think, she realizes that she probably can't accomplish this on her own so she looks for help.
which finally brings me to OP's point about the moment where vi reveals jinx's name to the council--and again i gotta say, i don't think this is poor writing or out of character. vi actually explains her own thought process: "if you really want people to talk to you, you have to let them think you have what they want." vi needs the council's help but doesn't expect them to give it to her for nothing, so when jayce asks about the grenade, rather than lying to him (which isn't in her nature), vi gives him a name. just a name, which if you think about it is pretty inconsequential. it doesn't actually help them find jinx. vi makes them think that she has what they want, even if she has no intention of giving it to them.
i've said this before, vi is not a chess player, she's a boxer. she acts and reacts step by step, choosing what seems best in the moment and then moving to the next thing. in the council room, her goal was to get them to mobilize against silco. if they decided to go after jinx next, vi would figure out that problem when the time came.
tl;dr i can see how these things seem confusing but it all makes sense to me the end