How to cohabit well

[Freeflight]

Just after some advice.
Marriage issues for a long time, infidelity on his part a long time ago, I never got over, resentment, all that jazz etc.

We've been in separate rooms for a few months and we are now getting along a lot better and coparent well. We are less and things just seem more content.
I still can't get on board with the idea of any intimacy though and so essentially we are a sexless marriage with separate sleeping arrangements.
I decided we need to make a call and define what we are a little bit, more to set boundary.
I've said that I want the separate rooms to be permanent and to recognise that right now, we are not a married couple.

Question is, how is best to do this/any tips.
We can't afford to separate further on the living arrangements because of all the mortgage rates and as we get along well it seems like this is the easiest option to still keep things as they are for the kids as we come to terns with things.

I don't want to end up in a different state of limbo because we are "separated" yet still living together, but I don't think that we can really sort an alternative yet so just want to make the best of what we can.

So far no nastiness, but I'm aware that can change quite quickly and unexpectedly.

How long has it been since the affair out of interest? It’s unsurprising those feelings haven’t gone away, the relationship is never the same afterwards.

if you’re definitely sure you want to separate, seek legal advice to get your ducks in a row and in the meantime make sure you have very clear boundaries. The best way to avoid any conflict is to have a pretty detailed conversation about how things are going to look for the foreseeable. For instance, are you now free to date others? The lines can become so easily blurred, and to be honest nothing will really change if there isn’t some kind of definitive action to end the marriage, even if neither of you can move out yet.

sorry you’re going through this, it sounds like a difficult situation.

Are you content to formally separate but remain living together? Ie tell people you’re not longer together and potentially date other people? If you’re both happy being single I’m sure you can cohabit for a while, but things will get complicated the minute one of you wants to move on.

The infidelity was 7 years ago, and I found out partially at the time, but he was never prepared to admit in full what happened.
I only found out the whole truth in June when I admitted that I was unhappy and still not over it.
He didn't really make attempts to amends for it, I think we just both buried our heads and hoped and resentment built.
We get along really well, but I don't find a physical attraction at all now I know exactly what happened (and I wanted to know so it's my own fault) and I don't see what we have as a marriage without physical intimacy.