Of course, your answer might be: “I’d happily spend the money on his therapy — if it were working.” And this brings us to the issue of progress. For you, progress would be a “change to his behavior,” yet you also say he has deficits in attention which lead to the very behaviors you understandably find so frustrating. (Attention-deficit disorder without hyperactivity is now diagnosed as A.D.H.D., inattentive type.)
Some people with A.D.H.D. respond well to medication, and if he hasn’t already consulted with a psychiatrist, exploring this possibility might be a limit you can set. But if it turns out that medication isn’t indicated — he’s tried it before with no benefit, or he can’t tolerate the side effects and medical risks at his age — then you might consider that the therapy is still helpful, not for mitigating his A.D.H.D. symptoms (which are lifelong), but for aiding in his ability to cope with them.
Recall that you left a relationship when your fiancé remarked, “How long will you be in therapy?” Your calling his therapy “superfluous emotional support” sounds like an echo of that. Your own therapeutic goals might have been growth, insight and tangible change, but what if he’s getting something else, such as emotional regulation, anxiety reduction, structure or a place to talk about important aspects of his life (aging, death, experiences he’d like to make peace with) in the safety and privacy of a therapeutic relationship? He might refuse to discuss his therapy with you precisely because he anticipates that you’ll tell him whatever he’s doing in there is “superfluous.”
Just as you found his previous therapist helpful for your goals, you might get curious about how his therapy has been helpful. Imagine, too, what his emotional state would be like had he not been in therapy. Notably, once he took a short break, he felt the need to resume, so he must find some benefit. And if you can appreciate even very small changes (such as his pivot to submitting the insurance claims), you might see his situation in a more expansive way that sits somewhere between “no change” and “significant change.”
None of this, of course, lessens your exhaustion with taking on a majority of the household management. For that, could you hire an inexpensive bookkeeper or assistant to free up some of your time and energy? Often I’ll see couples where one person is messy and the other neat, and when I suggest hiring a cleaning service they can afford, the neat person sometimes says, “But if my partner would just clean up, we wouldn’t need to!” True, I might say, but you didn’t marry someone neat. This is the partner you have. So you can get angry every day, or you can do something else.