I know you aren't OP but I follow youuu, so may I ask - what do you believe was most troublesome about Peter B's characterization in ATSV vs ITSV?
I've watched both several times, but do admit I took his character at face value and kinda just moved on a bit sad he wound up a bootlicker, but I know plenty have trouble with it.
ok I'm gonna try to answer this shortly bc I have homework I should be doing. but no promises bc you know me lol
So. In its simplest form. Peter B's arc in ITSV is about learning to care about things again, despite his fear of losing the things he cares about. In ATSV, they take away this development by making him seemingly-indifferent to the way Miles is being mistreated, the way Gwen is being mistreated, the bad calls Miguel is making, and the whole idea of letting people die for the Canon. It's kind of a subtle change, because they got his outward mannerisms right, his voice, his body language, etc--but there's an underlying callousness, I think, that trips me and a lot of other people up.
If we want to be more specific, we can look at his relationship with Miles. Its development was a huge focus of ITSV (maybe the focus of ITSV). In the beginning, Peter B literally couldn't care less about Miles. He physically walks away from Miles as Miles is telling him about how everyone in Brooklyn is going to die. He tells Miles to "go back to being a regular kid." His underlying conscience kicks in just enough that he reluctantly agrees to help Miles, but they're not friends.
Then, by the end of ITSV, Peter B is Miles's number one supporter. He's gentle with Miles when he needs to let Miles down: he says, "I know how much you want this, kid. But you don't have it yet." --And, when Miles asks for advice ("when will I know I'm ready?"), instead of giving the advice of "go back to being a regular kid," Peter B says, "It's a leap of faith, Miles. That's all it is--a leap of faith." Way different advice! He's trying to help Miles succeed, and being very very supportive and caring.
Then, of course, later: "I love you! I am so proud of you! Wait, do I want kids?"
Peter B's arc of learning to care about things again (even when it might hurt more to care) is realized through his learning to care about Miles.
And in ATSV, he only seems to care about Miles on a... surface level. From the beginning, his words like, "Don't worry about the suit, we'll get you a new suit!" (<-very rude thing to say about someone's outfit unprompted; didn't strike me as funny; might just be me) and "The kid wasn't thinking, that's not how he works!" ...seem to de-legitimize where Peter B was at by the end of ITSV. At the end of ITSV, Peter B was supporting Miles wholeheartedly, and in ATSV, it seems like they're... work friends that get along but don't really understand each other on a deeper level, or something. Peter B isn't stepping up the same way he would have at the end of ITSV.
Now, to be fair: I've said before and I'll say again that I think they can still make this work. Sometimes it is awkward when you meet up with friends again after a while! Sometimes you're on different pages! Sometimes things have happened to you in the interim that have made you see things differently than your friend! But I'm gonna need BTSV to put in the work on making me believe that, because the way ATSV did it feels sloppy and unintentional.
It's clear that Peter B's character was being used as a tool in ATSV (as all characters are, but we shouldn't be noticing it if it's done well) in order to help establish how Miles might have friends in the Spider Society, but he doesn't have allies (except Hobie). His callousness and backhanded remarks towards Miles when they first met up again were being used, story-wise, as a subtle warning towards Miles/the audience that Miles is on his own here, that he shouldn't let his guard down. But it's just... it's weird. It feels out of place with where we left off with Peter B's character. And much more importantly, it feels like a regression to Peter B's original state, before he got his character development in ITSV, which makes him feel flat and like the writers don't understand his character development. Which is not a good look, writing-wise.
I'll put it another way, for you: check out this deleted scene from ITSV. I believe (this is speculation) they cut this scene because they were thinking ahead to ATSV, and they didn't want to make the solution to the conflict presented in ATSV too obvious or on-the-nose. But it feels really really notable that this feels in-character for Peter B to do in ITSV, and in ATSV he is actively siding with the person who is advocating for the exact opposite ideology. Even if Peter B didn't say the exact words he said in this scene, this is an underlying theme of his arc in ITSV--remembering to care about that one person, instead of just thinking about "saving the world." That's what he learns. And in ATSV... that's gone.
TL;DR: In ITSV Peter B teaches Miles "You can't think about saving the whole world, you gotta think about saving one person," and learns to care about people and stand courageously with the things/people he cares about, even when it might hurt. In ATSV, he sides with Miguel "You have a choice between saving one person and the whole world; every world" O'Hara, and seems to have forgotten how to stand courageously with the things/people he cares about.