Oh dear OP, I know exactly where you’re at.
I had a partner who continued to post on casual sites, “without my knowledge”. He also swore it was all for fantasy and that nothing would ever happen.
So many times I found things on our shared computer, in the history. I was often able to log in to the sites to check his messages as he was very unimaginative with his passwords. It may take months, but always started again.
I’m sad to say I baited him once and he walked right into it. I joined one of the sites under a fake ID. When he was off work and I wasn’t for a few days, I arranged for the fake woman to meet him, so he texted me to say he was going to the bank with some mortgage papers, at the time I’d baited him to meet. I know he turned up at the meeting point and wasn’t at the bank until the following day. I never told him that.
I let it go so many times, I was aware he’d arranged to meet other men for oral sex but hadn’t gone through with it. Multiple sites over multiple years.
Until the last time. He always swore it was just fantasy, and I told him if he ever actually went with someone else I was gone. He did, I left.
The stupid part is I work in IT, programming and security. He knew I could check anything. I reminded him enough times – wherever you go on the internet you leave a little footprint behind.
He lied about meeting the woman (she came to our flat, in fact). So I tracked her down, emailed her and asked what happened. She told me enough. He was on a swingers site and she thought he was single. She left a glowing review of a genuine meet on his profile, which I read. I keep a printed copy of his profile, and some of the messages, just to remind me what a total shit he is on the occasions I miss him.
I'm happier now, and can only hope he's not doing the same to a new GF.