Agree with Grace. Either this (if you can confirm it) is a boundary or it's not. Each of us have to determine for ourselves how many "strikes" we are going to withstand, but serial infidelity is a dealbreaker for most people.
Enforce your boundary, and let him twist for awhile. If he tries to initiate any "what are you going to do?" convos with you, say something like "I have some decisions to make," or "I'm thinking about some things" and don't engage. A boundary explained is a boundary weakened.
Expect him to wipe his phone clean and then either try to show it to you or "accidentally" leave it lying around where you can find it.
