Listen, you are NTA. But finances are difficult between couples in ways they don‘t expect. My country faces lots of women in poverty needed subsidized housing and food stamps etc because of our „traditionally conservative“ ways. So during the past thirty years a lot of effort was made to get women into knowing finances and to analyse what happens and how to prevent women from falling into poverty. One of the major culprits is exactly the situation you described. Woman moves in with man. Man has mortgage to pay but he is also 100% owner of the house. Both agree because he owns that she will rent. Problem: She has no right to the house at all, only maybe that he fix things, and she can not buy or safe up either because of the rent she is paying. Couple breaks up. Guy has now house in his name that he could pay off faster because of the rent he was getting from her while she has no house, no right to any of it, no savings.
Is this economically ok? Yes, it is.
Is it also unwise for a woman(or any person, you can change genders but that‘s the standard setting) to move into the property of someone who you have a relationship with and by paying rent subsidizing their his mortage payments? Yes, it is.
The problem does not arise because any of you did wrong but because her rent becomes your property. And while this is absolutely economically ok, it usually gets thrown for a loop between romantic partners. If she was a random person you rented out to, she‘d have certain rights and you had certain responsbilities and had to keep out of their rooms etc. It would be purely transactional. But if you are a couple and building a life together, this usually becomes more complicated. In my country it led to women counting on their husbands to provide for them without ever having any real right to anything that was earned during their marriage. And when they divorced after 15+ years, the women lost everything, because he had the title to the house and mostly all the „big purchases„ like cars, despite them having contributed to the overall wealth of the couple for a long time. It‘s just that their money was burnt going into groceries, holidays, etc. So their contribution to the overall wealth never go them part of the overall cake.
Now, as for your personal situation: You only had been a couple for a short while. You did not mention any future plans. Also, she was dodgy and in the end very weird trying to make this into a cheating story. So, NTA on any accounts. But in case you have a gf with future potential move into your property again, try and have a honest and diverse talk about finances and how to manage the relationship interacting with financial planning on both sides.