you sound like a lovely mum.
If HE wants to do something about his sleep or mood, then he has an opportunity to change.
www.sleepio.com/ is useful for sleep problems - it's free for 7 days and can offer useful advice.
If he wants to engage with others (sounds like probably not in person), in a meet-them-halfway method, then a good online advice and therapy service (I have no vested interest), is www.bigwhitewall.com/ It is a combination of Facebook and a mental health service and is highly credible, I think there is a small monthly fee.
Research shows that (especially younger) people often engage with an online service more readily and in a less inhibited way than face to face.
However, it is possible that YOU may be able to do nothing, but if HE wants to do something, people will be there to help. He is clearly upset, depressed and potentially quite avoidant and anxious too, and sleep problems affect everyone badly.
The GP is a good call - they are the best service for crises, or as a method to engage with local services.
His ferocious intellect will be his strength as well as his existential achilles heel, but he is low - maybe it's a sign that he knows that things cannot carry on as they are, he needs more stimulation and interest than he is currently feeding himself with.
Good luck - thinking of you