When someone learns a motor skill, which part of the brain (or limb) is actually improving?

Say someone has never played piano at all before, but then after a decade of lessons can now play Rachmaninoff’s Third with the best of them.

Which part exactly of the body changed and improved? Did the fingers actually become physically more limber? Or was it all about rewiring some circuitry in the brains?

Fine motor control learning is done in the cerebellum.

Hence the fiction of “muscle memory.”

Destin Sandlin’s “Backwards Bicycle” shows this. Conventional bicycle, except with reversed steering functionality. Exact same muscles are used as for a fully conventional bike, but with practice, he eventually learns to ride it: