Again, I agree that therapy is her highest priority. She says she can’t get it. If she hasn’t exhausted all avenues, she should keep looking. Everything I read says that therapy and psychological/psychiatric services, free or paid, are swamped post-Covid. She doesn’t say enough about herself, school or employment or even living, situation to asseszs whether it really is totally impossible for her to find free therapy or reduce price therapy she can afford, or really any therapy at all. Some areas, especially rural, are bare of a lot of services that one can find in cities (if one looks very hard). I take her at her word that it is impossible for her, although I understand why you would doubt that.
Meanwhile, her fiance is a big anchor, perhaps her strongest now. If she pushes him away by refusing to plan wedding, because she is ashamed that she doesn’t have friends to invite, I think that makes her situation a lot worse. So, I think a simple marriage service, where few attend, is the best she can do for her self, right now. Yes, it would be ideal if she works on herself with a therapist first, but she can’t.
She doesn’t say a lot about her sister except: she walked off with the friends OP was starting to make through a hobby activity, when sister did a delayed walk into that hobby group. Why did sister do that? Does sister always keep a close eye upon her? Do her parents ask sister to do this? It just seems that sister could have left this hobby niche for OP to own. From what OP writes, she was having success in that endeavor until sister showed up.
Also, extrovert sister seems to be the primary person whom OP is negatively comparing herself to at the present time. OP mentions no way in which sister is a help to her. Actually mentions no way in which family is a help to her. Oversight or part of the problem?
It would be nice if OP updated with more info, but she hasn’t.