His therapist sounds horrid. Do you think a pyscho-therapeutic approach is appropriate, maybe he would do better with CBT with some goal setting, even if it is 12 year old goal setting. After all 12 year olds often do things independently and enjoy life.
I personally think if you reduce the pressure on someone to do all the things their peers are doing and just focus on what works for them in the short term to build confidence, making bread, growing seeds, posting a letter, going out for a film, perhaps just perhaps they might be able to take the next step. Most people don't want to be depressed, it is perfectly horrible being depressed even if you think it is a form of attention seeking.
I agree though that some external goal might help, but it might have to start incredibly small and unstructured so he doesn't feel he has failed if he doesn't go one day, and can pick up at the pace he feels able to. What about just focussing on getting him out of the house first, go to shops perhaps for an hour and see how he copes with choices for example in the shops (there must be something you need, perhaps groceries?) Often this can kick start a feeling of independence, just choosing pasta or bread, and the walk will do him good.
Also please please please check his Vitamin D levels. Give him 1000iu a day if you cannot get him to a doctor (25mg in laymen's terms) anyone who hasn't been on a sunshine holiday or out of all summer in shorts is likely to be mildly deficient at this age, especially if you are sallow or olive, dark skinned and it can make the symptoms of lethargy and depression much worse. As can B12 deficiency and folate deficiency. My son aged 16/17 had bad deficiency last year at this time of year, it was picked up only through chance, and certainly not suggested by any HP.