Wow, you just explained in details a phenomenon I've been experiencing without explanation.

Could it be same reason why I improve drastically after sleeping over a new skill?

Let me illustrate, the day I climbed a bicycle, it was woeful, I couldn't even direct my guess neither could I pedal but the next day it was all smooth.
I experienced something similar learning to play the violin.

And most of these times I dreamt doing the same thing.