Very helpful advice from @emmama2 ! I agree that your son may not be ready to knuckle down to studying. Taking a child out of school in Y11 is always going to be hard, but when he's so anxious about school, you likely don't have a choice.
I'd start by taking a step back. Don't panic about the exams. At school there is no flexibility to sit them later, and often no option to reduce the number of exams. Home ed is totally different. It's about the needs of the individual. Your son can do any number of exams he wants, at any age. If he needs to take a break, he can. Perhaps he will feel able to sit a few subjects this year and a few next year. Maybe you will register him for a few exams, but if he isn't on track to manage them, cancel and do it later. There's no particular reason to sit a large number of GCSEs at 16. Schools are under pressure to make kids do that so the school's "value added" can be assessed. Because of that relentless performance pressure at school, your son may well have absorbed the idea that he must achieve good results, and do it this year, or his future is down the pan. That isn't true. Slather on the reassurance with a trowel. Help him have conversations with adult friends and acquaintances and relatives who have done okay for themselves without getting good exam results at 16.
Meanwhile, focus on helping him recover by doing whatever he loves, whether or not that is academic. Does he enjoy drawing, martial arts, spending time with the dog, doing DIY? Whatever it is, encourage him to do more of it.
If bullying has affected his self esteem badly, he might not want to have much to do with his same-age peers at the moment, and perhaps he'd feel safer with close family, or adults, or younger children. There's no rush to chuck him back in with groups of teens.
Socially it is rather tricky to join the home ed community at this age. Compared with when they were younger, many of the other home ed kids his age will be spending more of their time on studies and less on social groups, and may be attached to existing friends and less open to new friendships. I doubt they would be actively unfriendly, and it's very unlikely they would pick on a newcomer, but teens can be a bit self-centred and may not go out of their way to welcome him. If he does crave the company of other teens, a special interest club or scouts or cadets might be helpful.
I expect that you, on the other hand, will get plenty of help and support from other local home ed parents, many of whom will have come to home education after their children suffered at school. People tend to be generous with their time. Be sure to join your local Facebook group and meet other parents of teens. They can answer all your questions about how to arrange exams.
Good luck! I hope your son starts to feel better soon.