No, you are not wrong. And you are not overreacting. Once someone has proven to not be trustworthy the onus is on them to earn your trust back. He’s trying to bully you into trusting him. There is a reason he doesn’t want you snooping - and it is that he doesn’t want to get caught.
You are not yet married or have children. While this does not diminish the love you may feel, it does provide you with a cleaner getaway. RUN. His behavior and patterns are that of someone who will cheat on whoever is unlucky enough to be his GF at the moment. Until HE gets therapy for himself and figures out what the heck is going on with him he is not fit to be ANYONE’S significant other. I know you love him and have been with him for a long time - but you need to pull a HARD 180 and begin building a healthy life without him.
I had a friend in a similar situation. The guy was cheating even before they got married - he said marriage would “change” him, he was WORSE after they married. About the time she finally decided it was killing her (and her health) to live this way - she found out she was pregnant. She lived with him 5 more miserable years while he repeatedly said he was “sorry”, go to one or two therapy sessions, decide he was cured and then start up again. She developed numerous autoimmune disorders from the stress and while she adores her daughter, wishes that she could erase him from her life... but she can’t fully because he’s her daughter’s father. This is a long way to say that I would not continue to commit myself to someone who clearly has SERIOUS issues. If he’s this bad now can you imagine what he’d be like going through the huge life stressors of being laid off, health issues, child rearing (if you hope to have kids), death of a parent, etc?
While many of us on this site, myself included, have chosen to rebuild our marriages after infidelity, our reasons are varied. Some have stayed because the vast majority of their marriage was really good, loving and supportive, some for kids or for financial reasons, others for a combo of the above or completely different ones, etc. I, for one, am actually really happy I stayed with my husband. We are happy.
But I’d be surprised if you’d find ONE person on this site who has gone through the tough work of reconciliation who would be willing to bet on your fiancé for a future relationship. Getting over infidelity and building a loving, trusting, fulfilling relationship is insanely hard. The more times they’ve broken that trust, the more lies and gaslighting, the harder it will be. You need to have HUGE reasons to even try.
Plus, he’s not even TRYING- he’s continuing to lie and gaslight you (making YOU feel bad for looking even though it always reveals things that are not right.)
You might want to consider doing some personal therapy for YOU and focusing on whether you really want this man. Sometimes we want something when it is taken away without really looking at whether it is actually good for us. I think if you could stop and look at him and the way he is acting as if he was a stranger, you’d be horrified and wonder why someone would even WANT to be with him.
I know you are hurting right now and I am so sorry. But this has NOTHING to do with YOUR desirability, how lovable you are or anything else. You are enough. There is some lack in him that he is trying to chase. But you can’t fix him. Only he can fix himself. And he has to want to do that - otherwise you are signing up for years, possibly decades of pain.