We were daunted by the cost of piano lessons so my son's introduction to learning music, which he was interested in, was Simply Piano on an ipad and an electric keyboard. The keyboard would probably be about £40 new but you could get one second hand. I thought Simply Piano was expensive but worked out only the cost of about 2 piano lessons for a year so we gave it a go. My son was very self motivated to use it and he worked his way through it for a couple of years and when he did start lessons (at age 10) he was nearly ready to take his grade 1 (which is not easy).
It is expensive supporting his interest - but school music lessons which he uses for his second instrument are £7.50 each week for a shared lesson and we pay £37 odd a term to hire an instrument. So that is within the reach of many. He also attends a free orchestra as well as a low cost one. He attends a junior conservatoire now which would be fully funded below a certain income level but we do have to pay the bulk of the fees - and we are not high earners at all but we are a two income household.
I guess I'm saying while you might not be able to afford a £40 a week piano lesson at this point if your kids are muscial you could try to see what you can do to start them off.
Whether my child (or any child) is "gifted" , or talented/high achieving is a matter of opinion but I was very conscious when my child was reading Charlie and Lola books at 2 (nearly 3 side of 2 for those books) that people held opinions like "pushy parents making kids learn to read before school" but we could not have stopped him learning to read. He read every sign on the roads/in the shops/the "rules" at soft play instigated by him - that's just what he liked to do.
My son definitely learns "differently" and can be playing complex music while asking what is for tea. He does well at school getting "higher understanding" or whatever the term is without doing any work at home and has whizzed through muscial grades without excessive practice - rarely practicing more than 20 mins in a day.
What I can say is he doesn't get his aptitude for learning from me and I do think his brain is "different". I do agree with people commenting that gifted and neuro diversity can be closely linked. The ability to learn in an extra-ordinary way kind of makes it inevitable that the brain is not ordinary and is different.
I think this is where "gifted" is different from a kid that achieves exactly the same outcomes but does it by studying morning, noon and night. Not that I am knocking that kid. If that kid is self motivated and wants to do that then they are great.
My younger son does have autism, has little verbal communication and is at special school (but he can play twinkle twinkle little star by working it out himself at the same age my big son could) so perhaps there may be something in the gene mix towards difference of brain and learning.
I believe gifted kids exist (did you see Lucy who won The Piano TV programme?) but that with their extra-ordinary talents there are likely to be differences that also include challenges. Families with gifted children are most likely also supporting challenges that are not necessarily visible.