I'm really sorry to hear what happened to your son. No wonder you are not sleeping.
My thoughts on this
Doing other stuff may not help him and people telling him to do other stuff may make him feel bad. Do you know or have any inkling as to why he was bullied? Has he any skin problems or features or anything that make him seem an easy target?
When I was going through a tough time (never tried to commit suicide as I was told from a young age suicide is never an option) I only wanted to be in my room. I hated socialising. I don't think people realised that when I tried to be normal, people would put me down. Being alone was really hard but far easier than being around people. In the end what helped me was finding my exit strategy. I moved away and being away was still very hard but I removed myself from all the people and hurt.
I look back and wish I did get out more but realistically that would have been the last thing I would do then. I'd rather have not been constantly asked to do stuff that society expects as I was obviously not the norm.
What you could do as a parent to keep the love flowing is just be there for him by not asking him to something that society expects of him, some people just prefer to be out of the way than in it full force and being bullied or put down because they're different. Cook his favourite meals often, hug him, tell him you love him. I really wouldn't keep trying with making him do stuff. Honestly that would have really upset me and actually it did.
Him going to uni shows he's happy to make an effort. Otherwise he probably wouldn't have applied and would have continued staying at home in his room. Maybe that's exactly what he needs, to get away from everyone and have a new start. He may still be quiet there but he won't be around the bad memories.
At this moment in time, you accepting him wanting to stay at home and be on his laptop all day will hopefully be enough to build his trust. Asking him to go and do stuff may be really upsetting to him and mean you don't get it. I would never have explained it to my parents as they wouldn't get it. There wasn't any point trying.
Hopefully this will ease your heart a little. Be there for him, don't keep trying with making him meet the outside. He will find his way.