My h has had very definite sex addiction tendencies, which I detailed ad nauseam in late January in a thread of my own.
I do think that the term is helpful, tbh. It doesnt matter whether it exists as a condition or not- what is useful is to see it as a framework which explains a person, NOT to excuse them or allow them off the hook for their behaviours. It helps to see what background factors make a person behave as they do, and also how it has manifested itself and what the thinking is. Usual infidelity reasons are less helpful, although the feelings are the same.
For instance, I could not understand my h kept saying that 'it was not about sex, but about power and control, and no sexual feelings were involved', even though he was talking to young women about their sexual histories.
Also, most sex addicts have other addictions, and this was the first time I was able to see his workaholism and passionate interests in computer games etc etc, as addictive behaviour.
Also, it helps to think about co- addiction- so, OP, it does seem to me that your behaviour may still be, in that the relationship is all about you supporting him, and an over focus on making him feel ok, in order that you can feel safe yourself.
Abitw- the things you have written about criticism etc, could have been written about my relationship. Years of me raising issues, followed by tortuous conversations about whether he is wrong about something/selfish etc or not, or whether in fact I am just a critical and controlling person to raise issues (eg wanting some help in the house, family time, not wanting to be lied to, not to live with the outcomes of workaholism, etc,) you name it.
It got to a stage where even when my own best friends and family were disgusted by him, I still wondered whether I was half to blame, despite the fact that I had entered the relationship as a confident single parent of 29, with a mortgage and a good education and job. I did not appreciate at the time that I was not just attracted to his charm, wit, and slight wildness, but that I WANTED TO FIX HIM. Of course, it could not be done, unless he wanted it himself, as I found out the hard way.
Even at Relate, when he did finally after a month admit the infidelity, he tried to blame me initially for it, because I had been critical of him, which made him feel 'controlled'.
We are in early days, post October/early November reveal, but he has changed dramatically, so far at least. If I were the OP, I would not reenter a live in relationship with someone like this unless I could see real evidence of sustained change, particularly towards yourself. And abitw, it does seem concerning that after counselling and your h's individual therapy he is still behaving crappily. My h recognises that he always used withdrawing as a tactic and now he deoes not do it. After 20 plus years, he has had to struggle to learn this. It is the least that you should expect.
I went to a girls night out a year ago, and a woman was talking about her young daughters relationship, which was full of rows etc. She said she had told her, it should just not be this hard to be in a relationship. That really stuck with me. Work, yes, to sort out problems which do arise, but hard work most of the time? It just isnt worth it. If I got back there, I would be off.