I’ve been in exactly this situation.
I let the emotional affair run a bit and didn’t say anything as I knew he’d deny it. Just kept monitoring the messages.
I was accused of being an abuser by him for checking his phone, so I’d avoid fessing up. He’ll just make it about your wrong doing.
the thing I learnt from it was that you don’t need ‘proof’ except to give yourself assurance that you aren’t going mad/ over reacting.
it sounds like you’re already using the info to make a decision about your future. I’d save yourself any more heartache or wasted time.
Or , if you really want to catch him- have they planned to meet up? Use the information you gather to engineer a way you can ‘accidentally’ catch them together. Or Why not just say, ‘ I saw you with X at Y’.
either way, just say you know it’s still continuing. ( no need to show proof) and that’s why you’re ending the relationship.
can I also say please don’t worry about leaving him- you’re already on your own. My life is so much easier without my exH. You will be happy. One day you might even thank him for this, as it’s got you out of a relationship with someone who has already checked out. You can meet someone who appreciates you ( if that’s what you want).
it’s hard to imagine right now, but one day you’ll be telling this story to your friends in the pub and laughing about his pathetic behaviour.