He probably was having an affair at some point - or still is. But given that you're separated, it's probably not or no longer really an affair - it could be he's got another primary relationship of some kind and is keeping you on the hook because he likes having someone who will listen to his self pity and it makes more financial sense for him?. It's very possible he phoned to tell you before you found out from someone else. The fact he wants comforting from a wife he's planning to divorce because his image at work is tarnished regarding a relationship he's had or hasn't had with someone else is totally delusional behaviour and so much more disrespectful than belching in front of you. He seems utterly mad. He wants to D in the future, isn't going to do it now as he wants you to be financially secure before he does, but also threatens you with D (which apparently is only a matter of time away anyway...) if you move away from him and act in line with the reality, which is that you live apart, you're separated for quite some time now, and he's probably had a relationship or is having a relationship with someone else.
But I guess none of this is about him, but about you. About why you might collude with his delusional, disrespectful and basically bonkers behaviour and what you might be getting out of it.
Is it in your best interests to delay divorce until you're on financially better footing? If it is, and you're willing to listen to his whining and let him use you for occasional emotional support until you do feel the time is financially right, then at least you can know you're acting in your own best interests. You say your future is tied to his job but also that he'd support his children and be financially responsible to them in the future. Are you in a gilded cage? SAHM's divorce, people who work minimum wages jobs and rent small houses divorce. Your financial future might not be what you imagined, and perhaps not as lucrative as if you continued a marriage to a high earner - and if that is what makes it worth it for you - well being clear with yourself about that might help you to tolerate what you need to do to have that more easily?
If the money side of things doesn't matter (it doesn't sound - especially if you have two houses and he has his own flat, that any divorce arrangement would result on either of you being on the breadline) then perhaps he's kidding himself about the real reasons for him delaying divorce. Perhaps you playing along with the pretence that he's keeping you in his life for your own benefit is not in your best interests and a dose of reality to him - which would involve you acting as if your relationship has ended, that his phones or social life or emotional needs are his own business and nothing to do with you - would be much better for you.
Or perhaps something else is going on here. There seems to be an awful lot of denial going on.
You are carrying on with your life - but things with your H are exactly the same as they have been for a long time. That won't change unless it no longer suits him (and he seems to be enjoying it cake) or unless it no longer suits you. Perhaps figuring out what you're getting out of it would help you in making a change in your own best interests.