Let me put it this way. What do you know for an absolute fact about the affair? Because I would suggest that everything else may be a lie. And if you quietly know that, it makes total sense that you would be paranoid and suspicious to the point of checking up on him.
it's so clear from your posts that you are in pain and hiding. 'Simplistic' responses are what you want, 'A few short months...' etc. There's a lot of 'don't lift up the rug!' going on. That's totally your choice and understandable.
But okay,so, objectively, it is totally fine to stay with someone after an infidelity. It's even okay to choose to stay with someone after an infidelity which has been lied about. but if you then are checking their platonic communication and they are in touch with the former lover you can be hurt but hardly be surprised. That would seem to me, to be par for the course of a lie agreed upon.
It is almost like you are LOOKING for evidence to confront him, but need it to be ENOUGH. It's painfully reactive. But does it maybe cover a private wish to be active? What about what you want? What about how you have been treated? Why are so frightened of what HE is doing or thinking? Are YOU even happy in this relationship? Or is it a distraction from thinking about that?
Cos it feels like you are going to go away from this deciding to keep your powder dry, that it's not worth it, and you'd rather stick to the lie agreed upon, his affair and your checking, unless you discover something that's 'enough'.
You already have been wronged and you don't trust your partner. Do you know why he had this affair? Do you really understand the extent of it? You need to address the stuff truthfully and properly with him that has made you feel that way, rather than wait crouched, virtually, for him to act in a way that 'allows' you to confront him. You are trapped by your own covert spying which is the only thing you are holding onto as your power and sanity, but really it's going to trap you and drive you insane.
But I know all that is harder to face than trying to second guess him. It's you who is disempowered. You who are clenching every time you log in. You who are fixated on his life without thinking properly about your own. You who carries all the stress and burden of the affair and the lies of that now. You don't need our permission to be angry with him for responding to her. You need to work out how YOU feel about him now in a wider sense, and act on that. You can do it.