I suggest starting with lead sheets, with melody and chords only.
The term "playing by ear" was always a pejorative when I was young. It meant some kind of illiterate flailing at the instrument, maybe learning rote patterns with no idea of how they worked together musically. (Think of little kids playing "Heart and Soul" with four hands - great fun.)
But what I think you are aiming to do is very different than that, and lead sheets can get you there.
When you take an improvisatory approach to playing - which IS what I think you are aiming for - two powers will help you, and happily those two powers aid in one another's development.
The first power is that of music theory, all the stuff you list in your question about chords and their relationships and scales.
The second is the ability to hear and replicate intervals and melodic passages without the aid of transcripted music.
Using lead sheets, or fake book music to begin will move you along rapidly to not needing any kind of manuscript at all.
Your left hand and the fingers of your right hand not engaged in playing the melody will dance to the tune according to the chord structure that is written above the melody line.
Getting over that hurdle of comfortably comping a melody - with just your sense of rhythm and a chord name to guide you - takes some time. If you sing, it can be advantageous to sing the melody, and occupy your hands with an improvised accompaniment. It is quite literally a dance your fingers perform according to the rhythm you feel.
Once you have mastered playing from a lead sheet, your ability to discard all manuscripts will follow. Playing by ear? Perhaps, but while deploying all your musical knowledge as you do so.
It seems obvious, but for me it was a hard won insight to realize that the music happens under my hands, not on any page. I make the music with my instrument, not because someone else wrote out instructions for me.
The great classical players absorb themselves in their pieces to the extent that they create the sensation in themselves and in their audience of generating the music in the moment it is being played, just like you would expect any jazz player to do.
Good luck and go for it.