Mh, I'm neither a Neurologist, nor any level of good at being a musician.
But it goes further than that. Now after a few years, I start to recognize patterns in songs and this removes a huge amount of cognitive overhead. For example, there are very classical rhythms in rock and metal. These were very intimidating two or three years ago, because it's so many notes to look at and a lot of them fast and it's just a lot of stuff to look at.
Now, on a guitar, I just recognize 18 bars of gallop-rhythm on string two and my right hand just does that, at least at the speeds I can do. Or you can recognize how a song is in a certain key and my left hand is just used to what happens in such keys. Sure, you need to learn the notes, but the physical motions are largely set already.
Similar things on a keyboard. In complex sections, a lot of thought can go into hand position and which finger to use to press a key, because you may need to prepare movement of your hand a few notes early or you can't hit a certain transition. I've noticed that something other than conscious thought optimizes that as well.
My biggest takeaway is that music is hard, and the human kinematic system is entirely amazing.