I agree with Irvine. She's obviously a bright girl. Who knows how bright? Definitely something to encourage at home. We have the game, Boggle, which DD (aged 5, in reception) loves to play. Hadn't thought about Countdown, so thanks for the idea!
Regarding her 'average' reading level at school, do you read different books with her at home? If you feel she is being held back at school and she wants to read a bit more, there's nothing stopping you from taking her to the library and letting her enjoy reading at her own pace.
My DD sounds somewhat similar to yours. Advanced verbal communication skills, vocabulary, reasoning, reading, comprehension. Grasps maths (and everything else) easily, though it’s not our ‘thing’ as a family so she gets less natural exposure. No social concerns. Nursery thought she was gifted but school weren’t interested in hearing what nursery had to say, and we didn’t pursue it.
We haven’t seen the need to try to label her as gifted in any way. All the signs are that she has the potential to do well at school, but beyond being an early reader and generally ‘bright’ I can’t see anything exceptional as to need to label her G&T at this stage.
You never know though. It’s a privilege to see a child develop and excel at some things. Enjoy it!