TBH I think it was wrong of him to share her feelings about you with you - where was the need? It's stressed you out and showed he doesn't understand privacy in a relationship.
I can share the POV as someone who is the gf in this situation. My DP had a female best friend (married, so I knew he wasn't romantically interested). I was excited to meet her initially and thought it a good sign he had platonic female friends. However she was very awkward when we met, kept cracking in jokes with him and not sharing context with me, kept pulling him aside to talk to him and generally being very possessive. I think she thought a decade long friendship meant she knew him better than any woman and had a degree of priority no gf could share. She'd keep butting into every story I had about us with one about how they had done it better sort of thing.
Anyway, her behaviour never changed. Despite me having no issues with them hanging out. And the more serious we got, the more jealous she got, and ruder she got with me. I tried everything to get to know her, to no avail, so my patience ran thin and I gave up.Think she just hated not being #1 anymore. That he wasn't just available anytime she needed him.
Eventually my bf got fed up of her behaviour and took space of his own accord. It's been 2 years since the last time she snubbed me and he's dropped her completely because her idea of friendship involved a level of control he didn't like. He tried to fix things but it seemed to him the friendship only worked when she was the #1 woman. But to him I am the priority, the person he's building a life with, and while his friends are important, he doesn't want competition for my role.
So my advice is - be friendly and welcoming. Get to know her, don't be territorial or rude. And accept that she may well become his priority as the relationship progresses. It doesn't mean he cares less about you. Just that he cares differently. And don't drag the gf into whatever anger you feel towards him, don't blame her, discuss things with him.