My teenager has a learning disability (not autism) and I feel that home education has given her the opportunity to develop better social skills than if she were at school. In the wider world, outside of school, there is less jockeying for social position, less meanness, less exclusion. So she hasn't been subjected to that. Though some people will tell you that you can't wrap kids in cotton wool and they have to learn to stick up for themselves, I don't think they learn that by being chucked into an overwhelming situation with no one to guide them. Besides, it's doubtful that they will need to deal with such unpleasant behaviour as adults. Adults have more options, such as the choice to leave.
So my daughter has high self esteem. She knows that she is just as good as anyone else, and that her worth doesn't depend on passing GCSEs or behaving like a cool kid. She has friends of all ages and abilities who like her for who she is. I am able to give her a lot of coaching on social situations. For example, she recently asked a teenaged male friend to go see a play with her, as a friend, and I gave her tips on how to ensure he knew it wasn't meant as a date. Somebody made some offensive jokes on a social media group chat, and I helped her come up with the words to shut it down assertively. We talk about money, who should pay for what, when and how to offer. If I notice that one of her friends is sad or annoyed with her, I take her aside and point it out and suggest how she could respond.
It isn't just me; she has a good community of helpful people to teach her. I expect your daughter does too, what with your large family. This is a fine place to socialise and learn adult skills, with people who love her and are in it for the long run. Maybe someday when she has recovered from her school experiences, she will have the energy and desire to make other friends, or maybe she won't feel the need for that. My daughter's best friend, who has autism, was perfectly content to spend lockdown with his mum and chat with friends on social media. I think it was over a year before he said he missed his friends and asked his mum whether he could meet my daughter in the park! But eventually he did. Now at 16 he is increasingly sociable and has friends round several times a week; my daughter is going round to his house later this evening for a film night. His mum keeps a very close eye out because he occasionally says or does rash things which might land him in trouble, and she's ready to intervene before it gets out of hand.
They're getting there, these kids. They won't be "finished" learning how to be adults by 16 or 18. That's okay. There is no rush. They get there in their own time.