I need advice, please!

So my girlfriend and I have been dating on and off for 6. I am lesbian, she is bi and I’m her first girlfriend.

The relationship was PERFECT for the first two years, no fights, sex all the time, oh I was great. However, after the two year mark, everything changed. She got bossy, controlling, started lying about little things, and stopped all sex and physical intimacy. It felt like we were just friends or roommates. For years I tried to make things work while also expressing my feelings, telling her I was feeling neglected, unloved, unwanted. She would tell me she would try to do better but never did. We’ve been in a completely platonic relationship for 3 years, which is a nightmare for me because I need PDA and sex and just physical intimacy in general. On top of all this, I have asked her to marry me multiple times and she accepts but then never wants to set a date. I am a very loving, romantic girlfriend. If she wants something I’ll get it for her, she is sick, I’ll take care of her 100%, I’m an equal partner as far as our relationship but I spoil her. I plan surprise dates, try to boost her confidence as much as possible, and invite her to all my family’s events do she feels part of the family.

But, because even after practically begging her to show me physical love, she wasn’t meeting my needs sexually/physically and because she kept giving the impression she didn’t want to marry me, we broke up and I moved into my own place.

In September, we got back together (but still living separately) and I just found out that in October she went to some guys house in the middle of the night to “help with his girl problems” something about trying to talk to him about why his girlfriend just dumped him. She says this guy was a friend from high school and hasn’t talked to him since then (approx. 15 years ago). She lied to me about going over to his house, about talking on the phone with him for hours and at all hours of the night, etc.. I can’t give the full explanation that I received because it’s too long but in my opinion, what happened was straight betrayal because she knew it would hurt me but she disregarded my feelings and did it anyway and then lied about it. She continued to lie about it and deny it even after I confronted her about what I had found out. She then confessed (though idk if it’s the full truth) but said she never slept with him but did find him attractive. She also told me that she thinks she wants a future with me too but she’s scared, but also doesn’t want to improve on the physical love that I need.

I want to try to make things work with her because I love her so much and I have always wanted a future with her, I just don’t know how to move past the betrayal and start trusting her again. Is it even possible? Or do I need to just cut all ties and move on? I also don’t know how to get her to start back with the hand holding and kissing and sex and other physical needs. Help please! I apologize for it being so long.