OP it is not your fault that your DH has betrayed you this way.
And it's important that when you confront this, whenever and in whatever way you choose, that you keep that in mind and you don't let him think otherwise.
You've done nothing wrong here.
However, you have reflected on and realised that there are areas in your relationship that have been lacking. They have not allowed your husband to behave the way he has, but he seems to be filling the gaps in your relationship.
From what you've said of him, other than this massive thing, he's a gentle and supportive husband. Beyond being a cheat, his worst crime is not communicating with you properly, or you with him.
You've assumed he's okay because he hasn't pestered you, whereas this probably could have been avoided with open and honest conversation.
Be careful now, OP. Often when something like this happens it will lead to hysterical bonding. This is a stage, after betrayal, where you will, for lack of a better phrase, fuck like bunnies. You'll throw yourself into the physical side of the relationship in order to prove that it's still viable. You'll feel a closeness that you haven't for a time, but it's just a plaster. It doesn't allow you to deal with the root cause of your issues.
OP, my advice is to approach him about this. In every other aspect of your relationship he seems like a good man. He appears to have been gently encouraging you, where he should have been outwardly talking to you. He's thrown in the towel and taken his attention elsewhere, but I daresay that's not what he wants.
Find some time just for the two of you. Tell him you know everything. Be completely honest and tell him you need complete honesty in return. If he lies, cut him off right away. Have none of it.
If you want to make it work with him, set yourself up for couples counseling ASAP. Tell him he has to cut her out of his life entirely and that you need him to be open with his devices until you feel satisfied that he's no longer betraying you. Offer him the same in return.
I give you this advice because it is what worked for me.
I am now at a point with DP where I don't want to look at his phone. If he stays late at work, I believe him. It's taken a lot of effort to rebuild the trust in our relationship, but it's possible.
If there's something worth saving, which it looks like there is for you, then you need to start working. Don't sit on this information and let it eat you up.
Good luck, OP.
You can always inbox me if you feel you need some gentle support.