tldr; partner 26m and i 25f broke up, we live together & r still cordial but i want to have sex with someone else and am afraid it will blow everything up

My 25F partner 26M and I broke up. I broke up with him. We still live together however, as we are on a lease, but he is planning on moving out. We have TWO bedrooms for each of us and always have. We sleep separately.

I've recently begun seeing someone and it's getting somewhere great, I think we are pretty close to being intimate. I never bring him to our apartment and don't plan to, but I do want to have sex with him next time I meet him at their place.

My ex partner is the only person l've ever had sex with, and he expressed that me having sex with anyone else would be the worst thing I could ever do to him and completely change how he looks at me. He and I are still cordial, our apartment is peaceful and friendly. Somehow I feel like I might be doing a horrible thing by having sex with someone and then coming home and being friendly with him who is oblivious. Would it be the right thing to do to tell my ex if that happens? Or is there no moral obligation to and I'm just creating problems for myself?

I really do like this new person, and I ended the relationship with my ex for a reason. The new guy knows the ins and outs of my current station. My ex and I are currently functioning really nicely as friends and I want him as a friend. What should I do?