The nursery should be following the EYFS framework. You said the head of the nursery said “they don't encourage learning letters, writing their name or numbers above 10 as 'that's reception level,'” It would be a good idea to take a look at the EYFS framework – you should be able to find it online. It’s been a while since I looked at it (my DD is in Y3 now) but I’m sure they are allowed to assess a child as ahead of their age category.
In my DD’s private nursery they had ‘letter of the week’ in the preschool rooms, and the fun activities would allow for a bit of differentiation. They wouldn’t teach things like correct letter formation as ‘standard’, but they were flexible to the needs and interests of specific children.
I was lucky because once my DD’s head of preschool noticed DD was reading nursery rhymes to her friends (she was a bit older by this stage: nearly 4), she offered to do a little bit extra with her as time allowed. They both enjoyed this (the lady had recently done a degree in early years development and was very keen!) but eventually she got to the stage where she said it’d be inappropriate to take DD any further, academically.
It’s a shame that your DD’s nursery seems so reluctant to encourage the more academically advanced children, but if your DD is happy there, I wouldn’t be worried unless they actively discouraged such interests, and made negative comments to your DD. She’s going to do well at school anyway.
If you are worried about your DD being bored at school, it’s worth trying to channel her enthusiasm for learning in different directions, so she doesn’t get too far ahead and find school boring. Learning an instrument, or sport, or computer coding, or a foreign language, perhaps?