My girlfriend admitted cheating while I was abroad

My girlfriend and I have been together since 2017 and moved in in our first apartment in 2020. Our relationship was pretty healthy until a few months ago. We have the same interests, similar upbringing, same humor, same friendgroup, the same sex drive and she's overall my favourite human. Sure, there were the odd arguments, but nothing major - just things that come up when you live together.
A few month ago I got a scholarship allowing me to study one semester abroad. This semester took place from the beginning of may til the beginning of august (this year)
When I came back to Germany, my girlfriend, who I thought I would marry one day, confessed to me that she had cheated on me at the beginning of july. With someone she met in a bar. It was a drunken one-off. She was having a horrible phase (lost one of her jobs, arguement with her toxic mother, depression) That really put a damper on things for me and it was an exhausting week full of arguments, tears, reproaches and wishing things would go back to the way they were before. We sat down together and I decided that I would try to forgive her.
After all, I love her endlessly and she deeply regrets her misstep. I wasn't angry either, more disappointed and scared. So we spent weeks trying to get our relationship back on track, but it wasn't like before. Despite many efforts, we had to admit to ourselves about 2 weeks ago that our relationship had become toxic and that we would work better as friends. In a clarifying conversation, we nevertheless stated that we still love each other very much and that maybe, after some time, there can be a return to normality. We both want so much for our relationship to work, but rationally we are not doing each other any good.
The problem is that we live together and the flat is in both our names. The current plan is that we both look for new flats and the one who finds a suitable place first moves out and the other keeps the flat (3-bedroom flat) and turns our current office/storage room into a second bedroom and looks for a flatmate.

The atmosphere in the flat is totally strange now because we still sleep in the same bed (our couch is not suitable for sleeping on). The housing market is terrible at the moment, so it will probably be a while before either of us finds something new. We're going to do some rearranging later this week and turn the office into a second bedroom (as a stopgap), as it doesn't quite feel like a separation when you're still so physically close. Somehow there is still a certain tension because of this, but we agree that we shouldn't have sex any more, even though we might feel like it. Neither of us can move to our parents because mine live on the other side of Germany, while her mother is a literal POS and her dad lives with his new wife in Amsterdam. We've been friends before becoming a couple so maybe just sleeping in different rooms will ease the tention.

I'd love to gain back my trust in her. She does everything to help and puts in so much effort but it's really hard to accept what happend. I'm trying but whenever she leaves the house after dark I picture her with another dude. I really hope that taking a break and not seeing each other romantically for a while will help. Maybe someone out there got some advice for me.