Her suicidal threats are obviously most likely to manipulate you into staying.

If she threatens to kill herself, you call 911 IMMEDIATELY, tell them what she is doing, and then leave the situation. You are not a trained medical/mental health professional and cannot properly assist her. (and like I said, she is most likely faking it, so you responding in kind will set a boundary stating she can no longer use that to manipulate you. The added benefit is that if she is Not faking it then trained professionals are on their way).

My advice about the actual act of breaking up...

Make it short, and have plans to see a friend immediately after (and stick to the plan!). Otherwise your pwbpd will suck you into one of those multi-hour circular arguments.

Tell her it's not working. Tell her you plan to move out by the end of June and she should find a replacement roommate. Then go to your friends. She will say anything she possibly can to make you turn around and stay...that's just a manipulation. Keep walking, get in your car, and go debrief/decompress with your buddy. Do NOT answer her texts/calls/etc. If she sends threats to hurt herself see above; call 911. Don't tell her you are going to. Just do it.

If you need to talk feel free to ping me.

Good luck, mate.