My H had a fairly short-lived EA with a woman last year. He was incredibly deceptive about it - I knew something was up and he lied to me and at times made me question my own mental health. It only came out for sure after I checked his phone and found evidence, then he told me what had happened in a gradual trickle of information over the next few months, all while still having sporadic contact with her that he was still lying about. The EA woman ended things between them and he still bumps into her occasionally at work - I no longer ask and he doesn't volunteer the information - and I have no idea what other contact they have.
I mention this because the hardest things for me were a) he never came and confessed to me, told me the truth, and in fact for a long time tried to say I was making it up, was being controlling, was having out of control anxious thoughts and needed to see a doctor etc and b) he didn't make the decision to end it with her himself, she dumped him and c) he did go through a kind of grieving process or sadness after the ending that I found nearly impossible to deal with.
Things have moved on since then and I don't think the EA is the problem between us - only a symptom and a catalyst for a lot of unpleasant behaviour from my H that is still a problem. But I think I wish I'd handled things more decisively at the time and went dark entirely until a) he was ready to actively and strongly choose me and a reconciliation and b) show some remorse for the pain he had caused me and some curiosity about himself and his own motivations. I do believe that without those two things, a rebuilding of trust and a proper reconciliation isn't possible - no matter how much he claims to want it.