Boyfriend has severe overthinking. How do I help?

I (22f) have been dating my boyfriend (23m) for two years now. At the start of our relationship, 4 months in or so, I betrayed his trust and went thru the drive thru that my ex worked at just to piss my ex off. I then lied out of fear for two weeks before coming clean. It was dumb and wrong, and obviously hurt my bf. I’ve been doing everything I can to make him trust me again, and it’s at the point where I’m his words, “he trusts me fully but he doesn’t.” Which I understand, kinda I guess. But we’re a lot better than we were when this first went down.

However, this has spiraled him into an overthinking mess. He was already one before we met due to being cheated on and cheating himself in his past relationships. He’s gotten a lot better, but it’s not really like where I would have hoped we’d be with it after this long I guess.

Some examples are:
-he’s always very suspicious about cars that drive past our house/our places of work more than normal
-he often sees “me” in cars and at places when I’m at work
-is quick to anger/anxiety if anything looks suspiciously placed when he gets home (ie I change my clothes and lay them somewhere to grab later for laundry, his brain jumps to come cheating
-is constantly angry and suspicious of our neighbor who moved in shortly after we did, bf thinks that he and I are doing something together with literally no proof other than neighbor somethings comes/goes as we do
-today I sent him a close up video of my eye as it was twitching weirdly and you couldn’t see it zoomed out. He told me that it made him anxious and overthink because I didn’t include a background and the background pose sounded different. the toilet was flushing so it sounded different.

And a lot more. I’ve been as patient as I can with him, have tried any and every way I can think of to try and help ease his mind or calm him down but it just ends up in us getting angry at each other. I’ve started snapping when he brings these things up, because usually he’ll either text me a long paragraph about what he’s overthinking and why, or he’ll just come home and very accusingly as me questions, like if anyone came over or if I went anywhere and his tone of voice is aggressive(he said it’s because of his anxiety/sometimes because he’s mad). I’ve tried asking him to please calm down before asking me so that I can think and answer calmly as well, but he then just gets more upset. Is it wrong for me to ask to be spoken to in a nice way? He says he can’t help the way he says things (his tone), but I’ve done it plenty of times when I bring stuff up.

No, we do not want to break up. We believe love is work and due to both of our pasts, our relationship was already going to be hard from the start. But i am more than willing to fight for him and his love because despite this he is genuinely an amazing man who has just had the short end of the stick all his life. And I know im making him sound bad, but this is really the only thing that is wearing me down and that we just can’t seem to get over. I know it takes time to get over stuff like that, but I guess I just thought we would’ve had more progress by now.

This isn’t all of it but the main stuff. Im happy to answer any questions to clarify anything, im not very good at explaining stuff so very sorry if this is unreadable.

TLDR: boyfriend is a sever overthinker due to his past as well as a mistake I made and it is wearing on me to be patient talking thru things with him. I want to know what I can do to help.

Edit: I also wanted to mention he does heavily struggle with mental illness and ptsd, his childhood was a very very rough one and it has taken a very big toll on his mental health.