Need an outside perspective on my complex situation, relationship history, and a "cheating" dilemma.

rewrote by Ai for the flow

​I want to share my story as objectively as possible to get some perspective on where I stand, including my own actions and faults. ​The Timeline: ​April - August: I met a girl from a different religious background. She initially said that she is agnostic and she’d change her religion for me but then backed out, saying she won't do it. Despite this, we traveled and had sex through May and June. In August, I found out she had sex with another man twice (once while under the influence of drugs and once while sober). ​September - Present: She moved into my room. We live like a couple in private, but she denies our relationship publicly. I handle all finances, cooking, and cleaning literally everything thing while talking criticism. ​My Faults & Shortcomings: ​I haven't been a perfect partner. I know I wasn't "enough" in many ways. ​I have a temper. When I get angry, I act irrationally and do things I later regret. I recognize this adds to the toxicity. ​The Breaking Point & The Dating App: ​Early February: Around her birthday, I felt my feelings for her had almost entirely faded. ​Valentine's Day: Even though I felt checked out, she told me she would "make my life hell" if I didn't get her a valuable gift. I bought the gifts, but I felt the relationship was dead. ​The "Match": Shortly after Valentine’s Day, I started talking to someone I met on a dating app (juat talking online about our lifes). I’m not sure if this counts as cheating, because I did it on the basis that we weren't officially together—especially since she had repeatedly refused to get back together with me despite our physical intimacy. ​The Confrontation: She found out I was talking to someone else. I didn't lie; I told her directly that yes, I am talking to another person. ​The Current Conflict: Once she found out about the other person, she suddenly claimed she has loved me from day one and was only lying about her lack of feelings before. She is now crying and very upset. ​The Impact: I recently lost my job. The official reason involved the sick leave I took to take care of her because we went to the hospital. I feel drained, guilty, and confused. I’ve supported her in every way, but the insults and physical hitting from her side have been constant until this recent "confession." ​Is it cheating if we weren't "official" and she had rejected me, even though we lived together? How do I navigate this guilt while being in such an exhausting dynamic?

ps. I see what I did as dishonesty not cheating since I was planning to hide everything till she moves out as planned since day one she moved in after she gets a job. she moved in in the first place bc she didn't have any money or job.

when I had feelings I never looked, even just looked to someone else, I never saw someone as much pretty as she is.

I asked her to try again if she really has feelings for my.

I never loved someone as I loved her.

ps. this is her side of the story: https://www.reddit.com/r/Advice/s/3UKD8E2Fft