My DS1 was also marked all the way through primary as requiring improvement in language & communication etc. We found this incredibly frustrating as at home would spout the most ridiculous things, such as at 5 declaring that his little brother was aggravating him and he talked non stop. He read excellently to a level 2 years above etc. However, Teachers constantly referenced the need to speak up more in class etc.
This continued all the way through primary. He's now in his first year at senior and has just received a report full of excellents with noted praise for his wonderful communication and understanding and his ability to put his points across well in discussion.
We spoke to him about how well he was doing and how proud we are.. but couldn't help asking ( very nicely) what the change was.
He told is that one of his earliest memories from school was a child sat near him answering a question in class. They got it wrong and some of the children laughed nastily. He had just never wanted to speak up in class in case they laughed. When he moved to senior, he went without a lot of his year group and with that went the fear.
I feel dreadful now that I didn't stop and ask him when he was younger about this. Of course we asked the 'is there anything worrying you?' Questions, but I guess he assumed we meant bullying. He was never bullied, he just didn't want to get something wrong and be laughed at.
You are just at the start of her journey. It's wonderful she feels comfortable to express herself at home. Fantastic she wants to explore reading and lovely she has a thirst for more... but maybe she's just not ready to showcase that to others yet. She'll get there soon enough!
Good luck OP, it sounds like you have a lovely, well supported child.