Really shitty of the poster who accused you of too much screen time. My own nearly 4 year old definitely has more screen time than his siblings did, we have been on lockdown for many months of the past year, it's hard, and there is nothing about this post that suggests the child is understimulated
. OP your DD sounds extremely bright, her maths skills are much better than my year 3 child (who I think has inherited my dyscalculia...but still
).
My 3 year old (nearly 4) has only just started to take a mild interest in writing his name but can't do it yet without tracing. I've just started with dry erase books, and laminated his name for a little practice but trying not to pressure as I can see he isn't too keen. After two summer borns who weren't ready for reading and writing in reception, I'm really glad my son is winter born and so I don't feel the need to push these things yet. We have toys with tweezers, I work on his scissor skills (cutting playdough is popular) and things like that but more often he's watching Waffle the Wonder Dog episodes on repeat, he gets cross if I even put educational nursery rhymes on.
Google X-ray of child's hand and pre writing skills. There are lots of great articles that compare an early years child's hand and a 7 year olds hand and explain why writing shouldn't be pushed, but I am guilty of pushing myself a little at times, I thinks we all are, and if I had a child so receptive to learning as yours I'm sure I'd be much worse.
Montessori sand trays are good for pre-writing skills. Helion toys and the Little Coach house have some nice handmade name toys. Also dry erase pencils are better than pens, and you can get tripod finger grips for them. But I'd hold off on that yet.