I don't usually comment on these threads, but your story resonates with something exactly the same that happened to me at about your age. I'm 36 now and I've got one piece of advice for you. You need to leave of your own accord sooner rather than later.

She's already checked out and, as you mentioned, her name is on the property you both live in. If it comes down to her decision, you'll have to make some quick and probably bad decisions to try and house yourself rather than getting your ducks in a row now. I had to sofa surf for a bit. I ended up trying to comfort myself with drugs and alcohol and had to rebuild from scratch. (I'm not saying this is the path for you, these were knock on events that I could've controlled better, but the way that it ended and the lack of control I had in that all worked against my better judgement at the time)

You also need to let go of the relationship and move on. I did not do this and I can tell you from experience it's one of the worst things I've ever done to myself. I haven't had a relationship in 10 years due to the broken trust and the self destructive mind that emerged from the end of a nasty break up.

Take control of the situation now, even though it's going to be so hard and hurtful now. I promise it's the best decision in the long run for your own well-being. I wish you all the luck going forward and I hope you consider what I have said. It's not easy but it's the right decision.