Her needs clearly aren't being met in school. This is causing her trauma and, if it continues, that trauma will harm her mental health. It happens a lot to children with ASD.
She may not have a diagnosis but she clearly has neurodevelopmental difficulties that have been recognised by professionals. Now those people need to be making recommendations for how her needs should be met in school and school should be implementing those recommendations consistently and effectively.
Masking can make it very difficult for parents to advocate for their child. You need to be clear that the while she is expressing distress at home, you will keep reporting it and they must accept that it is happening.
The strong bond with the TA is a positive that you could build on. Maybe she could go in and spend some time with the TA one to one towards the end of the day and then join her class just to put their coats on and come out. That's just a suggestion. You need to think about what sort of adjustments would enable to attend voluntarily. Having a quiet safe place to withdraw to might help. Also a visual timetable so she knows what is happening when, more movement breaks, less playground time, ear defenders to reduce auditory overload, adjustments to the uniform if it causes sensory issues, breaking down tasks for her, clearer instructions, less visual input from wall displays,... the list is endless and adjustments need to be tailored to your DD in particular; not just what might help a child with ASD.
Don't fall into the trap of tricking her into going to school and please stop forcing her. If you agree to pick her up early, make sure you do it, even if the school ask you not to. She needs to know that she can always trust you. If she loses that security, everything will be harder for her and you. My DD2's school wanted me to force her. The educational psychologist told them and me together that this wasn't safe or appropriate and they should make the adjustments she needed to be able to walk into school voluntarily.
You're doing a great job of advocating for her already. Keep going. Make sure everyone knows that this isn't separation anxiety as she can go to places where she feels safe without you very easily. It's school that is the issue here, not home or you.
If the school tell you that they can't make adjustments you feel she needs or can't bring in professionals to assess her and make recomendations for support because they don't have the resources, apply for an EHC needs assessment. School can do this but you can do it quite easily yourself too. Use model letter 1 on the IPSEA website. Fon't listen to any rubbish about how she won't qualify for one. It is not the school's decision to make. I'm happy to explain more about the process if that would be helpful.
Don't punish her or criticise her to not going to school and make sure that you're doing lots of fun activities that support her well being and self esteem during school hours.
Lots of parents are forced into home education because they don't have the resources to fight for the right provision for their child. Schools and LAs collude with this because, once a child is home educated, the financial burden of meeting their needs, which can be huge, falls on the parents. That's not OK.
Keep it clear in your head that this is not about bad behaviour. This is her communicating that school is an overwhelming and unpredicatable place and being there is causing her trauma.
Find some online forums for parents of children with ASD. Support and advice from people going through the same thing can be a lifesaver. It was for me.
Happy to talk more by PM if it helps.