She’s not “poly.” Poly isn’t an identity, it’s a relationship choice. She chose to cheat. She’s a cheater.

She might be inclined toward polyamory, but neither of you know that. Getting a crush is the easy part, actually maintaining two separate loving relationships is hard, and you have no idea if she could do that. In fact, her other relationship blossomed when yours sucked, so that’s evidence she’s pretty monogamous.

If you want to explore that’s fine but she should cut the “friend” off completely, then you two start reading books and stuff on what it means to open up sexually and romantically. That’s not controlling, that’s setting a boundary. You will not be in a relationship with someone that cheats or stays in contact with her affair partners. You were not open, she cheated, that bridge is burned. She does not get to play the poly card as a way to continue her affair, full stop.

Also, reading and learning here is fine, but you should also check out r/survivinginfidelity because this is still a cheating situation too, and a lot of those people have had a partner claim poly after cheating. Good luck.