I think I was better than most kids at math, particularly algebra, but those kids grew up and caught up and I suspect many of them are as good or better at math than I am. I know nothing about child psychology or anything adjacent, but I honestly think a lot of "advanced child" stuff is just maturity.
That makes me think back to my elementary school, where a lot of the kids who got into the "gifted" program just happened to be, surprise surprise, some of the oldest kids in their grade.
At that age the better part of a year in brain development can be exactly the "edge" one needs to excel. And then it can become self-reinforcing when kids gravitate toward the areas in which they dominate their peers.
My son is diagnosed with ADHD and high IQ and labeled "gifted". He's very immature, has absolutely no method, is very impulsive and can't maintain focus for more than 20 minutes. He seems very much less mature than his peers in anything.
Yet, he just understands and remembers every single thing at school much better and faster than his peers. So I guess technically that makes him "gifted" but it's not a very useful gift. It just creates problems at school because he gets bored quickly but cannot be given more work to do because he gets exhausted quickly too!
I read recently a title of an article that said "gifted children are special needs children" and that marched my experience.
Many are more expensive in time and money, but you may find fairly cheap alternatives.
Worth a shot at least.