my partner wants to enter into a second relationship with their ex, who hates me and is part of a group of people who regularly talk about how terrible I am behind my back (confirmed by three separate people so I know for sure it's happening). this makes me wildly uncomfortable. what does it mean for them to enter into the relationship despite knowing I'm not okay with it and never will be okay with it? is that technically cheating or should I be the one to back off on this?
You can't control your partner's choices, but you can control your own. You can say "I don't feel comfortable being in a relationship where Berthen is involved, even as my metamour. That is a dealbreaker for me." Then, armed with that information, your partner can decide whether or not to date Berthen. If your partner decides to date Berthen, then you decide to leave the relationship. Your partner has the right to do things you don't want them to do; you have the right to not tolerate that behavior in a relationship you're part of.
There is no such thing as "technically cheating," because what constitutes cheating is not a scientifically quantifiable thing. There is no secret safe in France where they keep the essence of cheating and measure various things against it. I would consider it a relationship dealbreaker if a partner of mine had unprotected sex with someone else. Not everyone feels this way, but that's one of my rules that, if broken, feels like "cheating" to me. Only you get to decide what boundaries are non-negotiable for you.