Me [28 F] with my boyfriend [31 M] of 2.5 years, texting ex issue

Hi! This is a crosspost and is on r/relationships too.

Ok, here's the story. About a year after my bf and I got together, I noticed a shady text message come through on his phone- and I want to be clear, he was showing me something on his phone, this text popped up with a brief preview and he closed it immediately. I didn't say anything, but later I did my own snooping investigation on his phone when he was in the shower and found a string of texts between him and his ex-girlfriend which were no where near appropriate. I, of course, told him what I found and that I looked through his phone - he apologized, said he didn't know why he was having these convos with her and promised me ALL contact with her would stop. From that point on, he password protected his phone and I thought OK, fine I crossed a line by looking through it - he's mad and put a passcode on - whatever. But, my gut instinct eventually started telling me he's probably got that passcode on there in order to hide something. I figured out his passcode easily by just watching him enter it one day. Later, again, when he left his phone unattended I went ahead and logged in and looked at his texts - he was still talking to her and still in an explicit manner - saying she's the only girl for him, he loves her, she's gorgeous, etc. (stuff he never says to me by the way). So, any other girl would break it off at this point, but not me - I love this guy and don't want to let it go. (Plus, as a side note, we moved out of our home state together which makes this situ a bit more complicated (and this ex, just for reference, still lives in our home state). So, anyway, I confront him again, he's severely apologetic, says he doesn't want me to leave him, etc. He says he swears it won't happen again and so I also say ok let's put it behind us and I promised I wouldn't look in his phone again. And, I didn't, until a couple weeks ago. I had some weird feeling and had the urge to look in his phone - no texts, ok good. But, I'm not stopping there, so I look at his instagram messages - and he was off an on taking to her there (recently)! - nothing explicit like previously though. The messages still bugged me and one of them he said "I dreamed about you last night" - and I'm like OK, what the hell. What is the point of this? Why is he messaging her still? Is it just for a thrill? I don't get it. It would make more sense if he was unhappy in our relationship or something, but he's never said or done anything to indicate he wants to breakup with me or is unhappy with me. I feel like I need to say something, but that will mean admitting again that I went through his phone and also I fear this might be the end of our relationship. Everything with him is great, and had I never snooped his phone I would be oblivious and happy about our relationship.

tl;dr: My boyfriend still messaging his ex after promising twice it would stop. I found out recently he's talking to her again by snooping his phone - what should I do