(writing as an adult student) I've gone at these topics with my teacher on and off over the years. My history is that when I was a child I was given a little keyboard organ (1960's), then a piano and and handed down sonatinas (Clementi, Mozart etc.) plus one Czerny, and no instructions, and nobody to watch play. I lost the piano at age 19 when my parents moved house, and got one again 35 years later. My "technique" was the worst version of what you'd get from this repertoire. It was interesting to learn that my grandmother, whose books they were, had been taught to keep her arms still, balance a penny on her hand moving only her fingers - and this was how I played without such instructions. Otherwise it may not have been the same as someone who is actually taught properly.
The connection to what you wrote is that my teacher and I determined that the repertoire I used also formed the resulting technique - it was "fingery". The rest of the results were simply due to an untaught child with a good ear ending up with rigid hands and hammering fingers. The remediation from that can be described as a gradual "unlocking" - starting to expand into space and 3D direction. If your music is mostly diatonic on mostly white keys, center of piano, mostly a maximum span of of P5, your hand tends to have a single, curved shape; you're not moving in and out of the keys much; balance in your body rarely plays a role. So .....
To balance all this out for me, we worked on the side which you say you were taught - the movements beyond the fingers. The repertoire chosen for this went all over the piano, had different hand spans, plenty of black keys, in and out of black keys, learning good use of pedal and applying that early. The repertoire (part of your post) went in the direction of Chopin etc. For a while I made my fingers almost passive, being transported by motions in the hands and arms. We used Op. 10 No. 1 - part of it and done slowly - to start making the hands and arms alive. ..... Some years later when I first went to a small sonatina, instantly the old rigidity kicked in from habit. I had to get the large movements and small movements to learn to talk to each other, if this makes sense.
Movement
There seem to be two camps. I think this is false. I think there is a continuum. There is individual movement in the fingers, and there is an impulse from further up since the fingers themselves get moved by tendons in the forearm (for most finger movements). If I move my fingers and keep my arms etc. rigid, it creates strain, so there should be a kind of counter-feathering with nothing being locked. You might feel it initiating from anywhere along the fingertip - arm - shoulder- body continuum, with it changing depending on what you are playing at the moment. There is also a chicken-egg scenario, it seems. Do non-tense fingers promote relaxed shoulders? Does "shaking the fingers into the keys" via somewhere in the back or shoulders promote nimble fingers? My own growth has been along these kinds of explorations.
There seem to be some tentative connections between my journey as a student - for both movement and repertoire - and your post, and that is why I've written this.