But she was never interested in him and never home so he was lonely.
I remember him saying how much his ex spent her time on social media.
These are important red flags. He's making himself out to be the victim and like he had 'no other choice' or 'did nothing wrong' by messaging other women while in a relationship. But obviously he was doing something wrong and he's not really taking responsibility for that.
You weren't present for his last relationship so you only know what he has told you about his ex's behaviour. Maybe she did go out a lot. Or maybe she didn't go out that much but he resented her every time she did. Maybe she wasn't very interested in him. Or maybe he feels ignored if his partner isn't hanging on his every word. Maybe she was on social media all the time, or maybe he was actually on social media just as much.
Either way, the healthy way for him to solve these issues would have been for him to tell his girlfriend he missed spending time together and wanted more nights together. Or to express that he feels she's not very interested in what he's saying sometimes. Or if she was really being a poor partner and out every night while ignoring him, the healthy thing for him to do would be to break up with her and look for someone better suited to him.
But what he did was get the hump and start cheating on her as payback for her perceived faults.
That's a major issue and probably part of why you're having bad gut feelings about this. The sudden declarations of 'never cheating' are also 'off' and you're right to feel suspicious about them. It's a classic technique of cheats to pre-empt suspicion by saying they would never cheat, as though words are truer than actions.
Like Maze, I would simply keep watching what he's doing, listening to your gut and trusting that your unease has a reason behind it.
It's also really important to be aware of double standards in your relationship. If he has told you he doesn't want you on social media a lot but is doing it himself, or if he gets antsy whenever you go out but expects to be able to disappear for days or weeks at a time with little explanation, or if he accuses you of ignoring him but actually does that to you a lot, this is a double standard. Double standards are used to control the behaviour of the other person in the relationship and are always unhealthy.