I found your posting interesting.To my own mind, playing naturally and being able to sight-read unfamiliar material has a lot to do with how much you play.
If you practice about 1-1/2 hours (or more) a day, you know where the keys are. You do not have to look at your hands. You know where the chords are. You feel them almost before you hit them.
Notes up on several leger lines, or the contrary in the deep bass -- you know what the notes are.
Your hands are strong and limber.Putting in significant practice time is crucial.
That will only happen if you love music, and if you have some input into what you are going to be playing. Enkindling a love of piano and of piano music thus is crucial.