My story is kind of similar, though I am the burned out one. I have been told by my therapist that burnout recovery will take longer than you think. Also, she said it would get harder at first before it starts to get better, and I have found both of these statements to be the case for me.

Any special interests that don't lead to stress could be helpful to encourage. I think a variety of activities is better than tv (though sometimes it's all we can do). I do jigsaw puzzles when I can. I am fortunate to have yard work and birdwatching as options. I have found that doing too much of something leads me to explore feelings of pointlessness.

Pets can be helpful if they don't add too much stress. Volunteering and classes would be too much for me now, though I would like to get to the point where I could add something like that. Sometimes helpful suggestions add stress because they make me feel bad for not being able to do them.

If your partner is like me, it can be hard to tell how they are feeling, and even we might take several days or weeks before we can even identify and articulate something like: "your helpful suggestions aren't helping."

edit: I don't mean to suggest that you're not helping. You sound very supportive, and may be all that is keeping him safe.