Nine year old says she doesn't want to live, school regressing

Our 9yo daughter has been saying she wants to die and questioning the point of life for about a year, and while it's very distressing to hear, I don't think she'd ever act on it. Outside of school she's generally pretty happy and laughs and plays with her best friend almost every day.

However, school has been a problem since year 2. We moved her midway through year 3 from a state primary, where she was desperately unhappy, to a much smaller private school that has a good reputation for SEN. Initially she was happier, then many similar problems began to emerge, particularly around the playground and socialising with other kids. This term seemed to be better until last week, when we got her autism assessment. She appeared comfortable with the diagnosis, but her fear of school has now rocketed back to the bad old days. Often she tells the teachers she can't breathe and has stomach pains. She won't accept the explanation that it is anxiety induced, and will shout at me for not caring that she is 'ill' (and should be let off school). I don't think there's any problem with bullying and the teachers seem very caring, plus she's now allowed to have fidget toys and sit and read outside the playground during breaks.

She says other kids don't want to play with her or ignore her, but until now she's usually been invited to all the birthdays and everyone she asks comes to hers (although she largely ignored them all to play with her best friend)...so I'm not sure that's the case. A consistent theme at both schools has been her saying she doesn't like the games other people are playing and they don't want to play hers. Another recurrence is fibbing, making up stories about things she's done or said. I've told her she doesn't need to try to impress me and that she shouldn't fib as it becomes hard to know when to take her seriously, but to no avail.

I feel most of her problems come down to low self confidence, so does anyone have any suggestions about activities, therapy or anything else that could help her? Academically she's doing okay apart from maths (which is its own psychodrama), but we've more or less given up on extra-curricular stuff. She doesn't really show any interest in anything except computer games and while she will try new things, she gets frustrated if she can't do them immediately, declares herself rubbish, and quits. She does like dancing, but again only on her own terms and not under instruction or a class.