Husband has been texting a ex an deleting messages I feel he is emotionally cheating but he doesn't whats your idea?

Before my husband an I got married he was texting a ex behind my back deleting messages I found out an confronted him an her she sent me screenshots of their conversations. He told her he loved her an that she was the one who got away. How I found out about her which he never mentioned her before was one night he was drinking with friends an got drunk on the way home he fell asleep we were playing music on his phone an i opened it up to change song an saw the message of her reply back to his message he deleted. We talked it through an fixed our issues or so I thought.
We got married was happy as can be till recently some very stressful stuff with my stepson came up. The other day I walked into our room an saw his messenger up I thought it was his mom or his best friend but it was her he told me as such okay no worries I told him i wanted to read the messages later as we made a agreement in the past if they talked i got to see to make sure no shady business was happen. Well I went to help our son with something come back an he deleted the messages all of em. I was pissed but I stepped away until i can calm down an then told him straight up I was mad an why. Well he made me believe nothing was wrong an yet my gut was telling me something was. I couldn't sleep for a few nights or eat it was eating away at me.
The woman he texted an me agreed that if I had any questions then I could ask her anything an she would send me any screenshots if I felt the need for it. So I did she sent me screenshots in them they were talking about their friend who died an was sharing pictures as she wanted to make a memorial that is all good with me I dont mind that. What I do mind is he wrote think about you a lot as well an how his biggest regret wasn't doing his promise to their dead friend to take care of her an how his drinking cost him his chance with her. She mentioned how he was happy with me an he said in a way that hurt me was that that the what if is always going to be on his mind
Husband has been texting a ex an deleting messages I feel he is emotionally cheating but he doesn't whats your idea?
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