No idea why you were downvoted. I have been a programmer and a musician for over 35 years, and I totally agree with your summary above. I use music as a recovery tool from programming because it prevents mental burnout for me. Both activities 'exercise' a different part of my brain to keep me balanced.
That's my case too, though I'm not sure that I distinguish between feeling and thinking. But playing music is how I recharge my mental batteries. Not only does it exercise a different set of thought processes, but it also demands enough of my attention that I have to stop thinking about work. And it also gets me out of the typical techie social milieu and into a wholly different cast of characters.
the analogy with "listen to music" is not "read the code" it's "use the program" but definitely composing and playing don't use at all the same skills as programming. For example it's easy for me to see where a bug is but when I compose music, I hear something sounds wrong, I don't know if it's "un-harmonious wrong" or "interesting wrong" and a piece of music doesn't "work" for me the same on 1st listen, 3rd listen, etc... whereas a program is by essence repeatable. And as a result I don't really attempt to "fix" wrong music if I feel I went wrong with an idea I just make a new one. Whereas with code I was debugging from the start, even when I was new and unconfident.