AIO for being uncomfortable with bf's female friend?

Hey all!

I am wondering if I am overreacting or not. So I have been with my bf for 4 years. At year 2 he met a girl who is also from his home country at a running club. They became friends. She would always complain to my bf about her own boyfriend. When I met her, after introductions, she switched to her own language and they talked with each other while I just stood there. I felt super uncomfortable but decided to be nice to her, and the next time I ran into her in the neighbourhood, I waved at her and said hey! She completely ignored me. This happened twice.

She broke up with her boyfriend. Now she's single and wants to take walks with my boyfriend. He asked me if he could introduce her to a shared game of us. He told me before that he would consider it cheating if I introduced a guy friend of mine to this game, as he said it was just for us. Now he wanted to invite her. I said I was not okay with that. But I feel even more uncomfortable with the situation, that he wanted to introduce her, and the double standard.

Some other points: I asked my bf why is he friends with her, as she only talks about her dating life and herself (my bf complains about that to me). He said: she is from my home country, I don't have any other friends from there, and she is super sweet. I also once overheard him mention to a guy friend of his that "guys at the running club were constantly flirting with her because she is so pretty" and that he could "smell her sweaty pussy" which I also thought was a crazy thing to say. Third mention: at her birthday party he paid for all her alcohol, he never send her a tikkie, it was expensive and we are not rich. Also, he calls her nicknames like "mija".

I really dislike this situation. AIO for not being comfortable with their friendship? He says he is just being friendly, and that she would never be interested in him. He says he likes to take care of other people and that I am acting jealous and controlling deciding who he can be friends with.