I agree @crumblingschools the conditions in many places are very difficult. However, the OP's 6 year old dd felt uncomfortable about the way she was spoken to and the OP listened to her to ensure that she is treated fairly and reasonably in school as well as ensuring that her dd is behaving well. At the age of 6 the dc did not understand why the TA had spoken harshly and she did the best thing possible, she asked her mum and had a conversation about it.
This is good parenting. The OP didn't go to the school to abuse the TA or be rude, she had a civil conversation to make sure that everything is ok as is her responsibility as a parent. Problems do occur and parents do need to look out for their dc, although this should not been done in an intimidating or unreasonable manner.
It's awful isn't it. Grown adults are expected to creep round them for fear of offending their delicate feelings. Setting boundaries is considered abuse. Please, thank you, sorry and excuse me are considered optional. Polite eye contact is optional. They cry at the drop of a hat. NO is not a word in their vocabulary. They can't be left at a party/Brownies/Sunday school without a parent mollycoddling them. And the current/future generation of parents is feeding into this. I dread what is to come in 10/15 years time.
This is hyperbole. The world has changed in the last 15 years and there could be many reasons for children behaving the way they do nowadays. For example, "Polite eye contact is optional" is an interesting observation. There is much less opportunity nowadays for dc to actually speak to grow ups that are not close family. State schools instil a 'do not speak until you are spoken to' culture and children are generally always accompanied by their parent or carer when out and about so do not develop those conversational skills until much later, if at all. This is exacerbated by much social interaction taking place online rather than in person. But I am digressing.
Regularly shouting at children is abusive and unprofessional. But we don't know if the TA in the OP does this and anyway, the TA is now being nice to OP's daughter, so the OP did good. If her dc feels happy and safe in the classroom, it will impact positively on her learning. Should OP find that her dd is extremely sensitive and crumbles under any perceived criticism, she'd have to tackle that differently and build up her resilience. Resilience is not fostered by treating kids in a stern and intimidating manner.