I think depression along with potential unresolved issues from his past is playing a big role here especially with the mention of how the therapist was fixated on past family trauma. But you can only extend so many olive branches, if he refuses to grab on and continue therapy, then I believe some hard lines need to be drawn.

Does he fully understand how this whole situation is affecting you? If not, then you should make that clear to him. If it's gotten to the point that you're considering breaking up, he needs to fully understand that. If you do break up, it shouldn't come without prior notice, he should fully understand why you're breaking up before you choose to do it.

But before that, get him to write up a life plan and emphasize the areas of his life that need improvement. Based on what you've said, he needs to go to therapy (I would prioritize this above other things), he needs to build and maintain a proper social life, and he needs to make a clear effort to pursue some type of work that he likes doing and could see himself doing into the future.

Obviously, these things don't improve overnight, but if he develops a clear plan for where he wants to be and for improving these areas, and he makes a committed and sustained effort towards that plan, then that would be huge progress.

The way this affects you and your relationship with him should be emphasized, this isn't just about him being stuck in a rut, its about the future of your relationship. I normally hate ultimatums, I think they're unfair and usually unnecessary. However, if he doesn't make a committed effort in these areas, then he needs to understand that this relationship cannot last. As harsh as it may sound, if it comes to it after trying everything else, even if it's your decision, it's not you ending the relationship, it's him (assuming he fully understands what's at stake).

As far as the life plan idea, give him some time to fully flesh out his thoughts and to research what he wants. Don't let him take too long though, you don't want him slacking with this as well. You can also probably go on YouTube and learn about how to write a life plan and what it entails. You may want to write one yourself too so you both can compare notes and see how compatible you are into the future.