I've encountered a worse version of the instrument bug. If you get the bug while grabbing the instrument in Eagle's Tower, when you close out the game and re-open it the door to the instrument will be closed but the boss is still defeated, I can't find any way to open the door now.
just managed to do the same thing, looks like my run is over lol
EDIT: do what this guide says: Instruments soft lock solution - Link's Awakening DX HD community - itch.io
(for the piano it was "s objectXX instrument6:1")