It's funny what you said about Carol re: Peter, because Peter, I think, is also falling head over heels for Carol way, way faster than he could've imagined. In a backwards way it's the casualness of their interaction that makes it so emotionally intense. Being around Carol is so... simple. He feels relaxed in her presence, feels like she brings out the best in him: he's funnier, more pleasant, more honest, more the guy he wants to be. He feels safe with her, though you'd have to start pulling out teeth before he'd admit it out loud in quite those terms.

The elephant in the room is that as much as Peter deeply, genuinely cares for Carol, he's still hung up on MJ (maybe always will be), and the fact that one relationship was in one universe and one relationship is in this universe is letting him stay in denial about whether that emotional standoff is sustainable in the long run. And speaking of denial, emphatically not thinking about how they could both go home and not remember anything about being together and never get together at all in that universe, oh no.