OP, I have experience something a little similar med my DH.
I think that many men tend to become depressed when they are ill, feeling that they can no longer pull their weight. This may not be anything a doctor would diagnose as depression, but more what we all used to call "feeling depressed" when we were young.
You need to help him get out of the rut, he is in. If I understood you right, his back is a little better now, and yes, start by getting him back to the table for meals.
Then point out that as you are still working, you would appreciate a little help with the housework. Frankly, asking a man to dust is NBG, as they don't see dust.
Ask him what tasks he feels up to doing, and let him get on with them. If they are not done in the specified times, point out to him that you are waiting for him to do them.
If you can, get him out for a walk every day. We have just bought new electric bicycles and it has made an immense difference as DH is fonder of cycling than I am, but I am happy to go on my bike, as it means he is exercising.