iternabe Your point of relearning body movement for piano playing applies equally to everyday tasks is so true! One of the first things @Seeker instilled in me about relaxing the shoulders. I then become aware that I am guilty of tensing the shoulder in some of my other activities as well, like when I am typing, or holding the milk pitcher when steaming it on my espresso machine. It will take some period of consciously correcting it before relaxed becomes the normal default state.
My awareness started (oh my!) 20 years ago at the end of the violin period. There was an explanation of a stance because of the weight of each arm over a foot. I felt nothing like that. My posture was lordosis, arching the lower back and that's where I carried weight. I'd always had back ache after walking, and was starting to need a cane (in my 50's). I'd go to the woods and throw sticks, aiming to feel it move into the respective foot. With a personal trainer, doing standing curls, it was to feel the weight come down a leg into my feet. Later it was other things: breath to stabilize the torso. After I walk it feels like a massage, and I can do slow jogs. (71 now).
That lordodic posture can also affect how you use your arms, and the old "shoulders back and down" "advice" is deadly. My shoulder blades were jammed together and tight - they should be able to glide with arm movement. For a while I practised "stirring a pot of soup technique" ๐
To make it less complicated:
If I'm using my body badly in some way, then certain everyday activities can betray this, and doing "too much" of that activity could then make you stiff for when you go back to the instrument - because of how you did it. Of course you can also just do too much.
The cool thing about this side of it, is that you can practise movement while doing everyday activities.