I'm sorry op but I think it's a really bad idea if he moves home at 33 years old. What on earth will extending his adolescence or semi-dependence on you actually achieve?
You have an opportunity to draw a line in the sand right now.
Paying his mortgage won't help either.
You've already got him a job and he has scuppered that. Now is his opportunity to find a job he likes and is engaged in.
I say this as a parent of an adult child with autism. I am the same age as you too. Anything could happen to us, and our health, and we are not doing our adult children any favours at all by allowing them to rely on us and not stand on their own two feet, which will ultimately bring them fulfilment and a bit of pride in themselves.
Children who are ND do take longer to reach maturity and independence but allowing him to give up and become more dependent on you isn't going to teach him anything.
I have the greatest of sympathy with him if he is depressed and his executive function is suffering as a result, and as a result of his ADHD, but he needs to try and help himself at least to find strategies to manage his life. Take ADs perhaps? Get assessed. Assess his daily routine. Eat well. Sleep well etc. Get in to a good routine where he can make changes in his life.
Op you were parentified as a child and because you didn't want this to happen to your children; you've gone too far the other way. And you are continuing this pattern now and sorry to say but this over involvement in your sons' lives could be actively harming them.
Can you examine yourself honestly to see if part of you doesn't actually get a kick and some fulfillment in being needed by everyone all of the time? It's not a crime but lots of people like to be needed.
Sorry to say this op but when you mention that you supported your therapist, all sorts of alarm bells rang in my head.
I had a relation of mine say this to me once and suffice to say his image of himself as the caring, rounded, put upon keystone of the family on whom everyone depended, was very far from the reality of who he is.
He actually is quite a needy person himself. I'm not saying this applies to you at all but please consider the possibility that part of you does get something from this over-interdependence with your adult DCs and looking after the therapist was a convenient way of diverting attention away from any issues you may have. A good defense system.
I know you have started this thread saying you want to be free of responsibility but are you sure you are not giving mixed signals to your YA DC? Finding jobs for all three of them in the first place is fairly unusual surely?
Op I can understand your anguish leaving a YA in their early to mid twenties to soldier on alone when they are struggling, but a young man of thirty-three? Really?
In your shoes I think I would announce that you are going away to stay with family for a while, if your job permits, and leave them all to it. You probably will find that they get on reasonably well once they know you are not there as a fall back option.
Edited to say: have just read your update about the ADs. That is a good sign.