I don’t think I can trust my partner—am I overthinking or is it time to leave?

Me 26F and my boyfriend 27M have been together for 3 years, and I’m starting to emotionally check out of the relationship. The issue of phone privacy keeps coming up. He has a thing about keeping his phone private, but the 2 times I did go through it (with his permission), I found things that concerned me—not cheating, but still shady. Each time, he snatched the phone back and gave excuses. We haven’t been intimate since, and part of that could be due to my pregnancy (I had HG), but it’s been hard to feel close or trusting. He checks my phone often and gets suspicious over harmless messages, yet won’t let me do the same. He talks about marriage, but I don’t feel like I fully trust him. I don’t think he fully trusts me either. I’ve suggested we sit down one night and go through each other’s phones—not to accuse, but to rebuild transparency and trust. I just want honesty and mutual openness. I know my insecurities play a role—I’ve been lied to a lot in life. But I also think trust and transparency should be a given when you’re talking about marriage. So now I’m stuck:
Do I walk away because I don’t see myself fully trusting him?
Or do I stay and try to work through it—even though emotionally, I feel like I’m slowly checking out?

tl;dr:
Been with my partner (M27) for 3 years. He won’t let me go through his phone without getting defensive, even though he checks mine. Found some concerning (non-cheating) stuff before, and now I don’t fully trust him. We haven’t been intimate in a while, and I’m emotionally starting to check out. I just want transparency if we’re talking about marriage. Do I stay and try to fix this, or walk away knowing I may never fully trust him?

Would love any thoughts/advice on the situation.