to want to stop talking about infidelity.

You've clearly damaged him and hurt him terribly by cheating on him. He sounds a bit stuck in it. Maybe suggest some counselling for him, so he can hopefully work through it and move forward? I wouldn't expect him to come back to you though.

Not that it’s any of your business, but no—I haven’t.
I just happen to believe that people make mistakes, and long-term relationships sometimes go through things that aren’t black and white. I can understand how hurt and forgiveness can exist at the same time. That doesn’t mean I’ve done the same.
It’s perfectly possible to have empathy and still hold someone accountable—both things can be true.

Well you’ve defo cheated

Yes, it would be absolutely lovely if he could move on. I'm sure he'd like that too. But he can't, so that's tough. You have to deal with the situation you have not try to bend other people's emotions to fit the one you want. You have two choices. Accept he needs to do this and shoulder that as the consequences of the hurt you caused, or tell him if he doesn't stop bringing it up your friendship with him will have to end. Tbh I think some distance would be best anyway. If your connection is preventing you both moving on separately, but the cheating is preventing you moving on together, you're both stuck in an unhealthy limbo. The decent thing here would be to move away from him and give him space to heal. Because at the moment, you're an open wound.

YANBU at all. You've been through it, and through it again. It's been nearly 20 years since the infidelity, and you've stayed, you’ve shown remorse, you’ve rebuilt trust (or at least tried to), and you’ve never repeated the mistake. That says a lot.
At some point, he has a choice: either he starts to truly process and move on from this—possibly with help like counselling—or he needs to accept that staying so close to you while still harbouring that resentment is only hurting both of you.
It’s not fair that every day he brings it up, especially after all this time. That’s not healthy for either of you. And if he can’t let it go, then some space might be necessary—not as a punishment, but as a way for you both to move forward with your lives, whatever that looks like.
You’re not asking him to pretend it never happened. You’re asking for peace and progress—after nearly two decades, that’s not unreasonable.
If you're to have any kind of real friendship (or anything else), he needs to deal with his feelings in a constructive way, not keep punishing you indefinitely. You can’t do all the emotional heavy lifting alone.
Stay strong—you sound thoughtful and fair.

How easy it is for the one who cheated to tell their partner to get over it.

“couldn’t cope with the thought I’d be unhelpful”

You sound inherently selfish. You need to stop being close and thinking you might get back together. He wouldn't be able to get over your cheating, and constantly worry you’d cheat again, you would most likely get bored and cheat again.

distance yourself and only communicate about your co parenting and children.

You have obviously not regained his trust and he is still hurting. How would you feel if he had cheated on you bur wanted you to forgive and forget?

Well, it might be better if he could forget about it but clearly he can't, and that was the risk that you took when you cheated on him. I get that it must be annoying to be constantly reminded about what you did, but you can't tell him how to feel about it or demand that he pretends it never happened. You do have the option of distancing yourself from him further if you're finding it too much.

The closeness is the problem here, not the infidelity. You said it yourself, it’s holding you back. Cut ties apart from those necessary for co-parenting and move on with your life. You can’t ensure that he comes to terms with a 20-year-old event. And tbh, it sounds a bit mad for an ex to be still mentioning daily a 20 year old infidelity when they’re no longer in a relationship with the person.