27F 29M BF messaged another girl while out of town.

I went through my BFs phone today because he left it at home. Back in March this year, my BF violated my trust multiple times. He basically gave me free access to his phone, saying I could look through it at any point. I never had until today.

I found a message from back in March this year (after all of our trust issues) where he messaged a girl saying “hey stranger ;)” at 12am while he was out of town on a boys trip and in her city. She never replied. Him and this girl had previous history.

I confronted him and he said that he was drunk and was looking to meet up with her. That he felt guilty immediately after he sent it. I also found messages of him accepting a DJ gig at a club with dancers after he explicitly told me he wasn’t going to accept it.

I know what I should probably do. I just dont know if that message alone is grounds for a breakup. How should I proceed moving forward?