Does she seem genuinely sorry? Or just sorry she got caught?
Had there been any signs that things weren’t ok between you?
Is the guy someone she spends time with eg at work or someone she found specifically to have an affair with?
Sorry for all the questions, it’s just without a bit more detail it’s difficult to know how to advise.
For example if its someone she works with she really needs to look for another job so that she’s not in daily contact with him. She needs to cut him off completely and be totally transparent with her phone/social media etc while she earns back your trust. You shouldn’t need an app to check up on her, she should understand that she needs to be willing to show you her phone at any point and that she’s broken your trust in her.
There’s a Shirley Glass book that’s often recommended for the spouse who has been cheated on, but I’m not sure if it’s mainly for emotional affairs rather than full on physical ones. Also I presume it’s mainly aimed at the woman who’s usually the one being cheated on, however it may still be worth a read, as she advises what needs to be done to overcome the betrayal. I think it’s called Not Just Friends.
I’m sorry you’ve had such an awful shock and that your DW didn’t own up to it when confronted, but compounded it with lies. Often that can be just as hurtful.
The feeling of being closer is called hysterical bonding (or maybe it’s testerical if you’re a man?!) but it may not last, it’s a survival instinct to keep your spouse from disappearing while you deal with things. Be kind to yourself.