Girlfriend threatens me to kill herself if I meet any of my friends in person

Basically, the title sums it up. My girlfriend (23F) has sociopathic tendencies and doesn’t want me (24M) to see any of my friends. She believes that a relationship should be the only meaningful connection a person needs. I, on the other hand, want to maintain healthy relationships with people I care about. I don’t think being in a relationship should mean cutting off your friends.

Recently, she gave me an ultimatum: if I go out with my friends, it will hurt her so deeply that she says she will commit suicide. Ordinarily, I would break up, but she threatens to kill herself if I do. I can’t bear the idea of living with the guilt of someone I once loved taking such an action. At the same time, I feel trapped in this relationship, which makes me deeply unhappy and suffocated—like living in a cage. How should I approach this? At this point, I'm totally clueless about what to do.

For some additional context:

She refuses to go to therapy because, according to her, “she is normal; my need to have other people is something weird.”

Her logic is something like: “If you go out with other people, it means you prefer spending time with them over me, which means I’m not the most important person in your life.”

Edit: I know that leaving this relationship is the only option, don't worry. I'm asking about how should I approach leaving a suicidal partner. I know that this relationship is toxic and it's impossible to get it on the right track at this point.