I Broke My Best Friend's Trust and Now I'm Not Sure Who I Am Anymore

It's been about a month now since the incident happened with Sarah. We've known each other for over ten years, practically grew up together. I remember we were both single back then, but it was clear she wasn't interested in me romantically and vice versa, or so I thought. Last summer, after a long night of drinks at the bar, things got hazy. One thing led to another and next thing I know, we end up back at my place. She’s been drinking too, clearly not herself. The next morning, everything was awkward. She avoided talking about it, acted like nothing happened. For weeks, I tried to play it off as a drunken mistake, but deep down, I knew it wasn't just that. There was something there, even if we both ignored it afterward. Over the past month, Sarah and I have barely spoken except for brief hellos in passing. She's distant now and I feel like a complete stranger whenever she's around. The guilt eats at me every day because while it wasn't outright forced or non-consensual during that moment of weakness, it still crossed lines we should never have. What if she feels the same shame? Am I an asshole for crossing this line even though it seemed mutual in the heat of the moment? I don’t know how to fix things with her. Should I reach out and try to talk about what happened or give her space and time to heal from something that might never go away? I’m stuck between trying to atone for my actions and hoping she’ll forgive me, or cutting off contact completely because I don't want to risk more damage. How should I handle this situation with Sarah?