I have sometimes wanted people to notice my cutting, and sometimes not wanted people to notice it.

It sounds very invalidating to have her say that, as someone who has cut for 12 years but not in the past few months, you do not meet that criterion. Same for sui.

I would not see a therapist who held the view that "BPD people love drama." Even if you manage to convince her into agreeing with a BPD diagnosis, even if she manages to change her opinions on things like BPDers & drama, I doubt that she has the skills and mindset you would need to actually make therapeutic progress.