I can't delete songs from my music library

This is an extremely annoying behavior. I recently bought a new M1 Max Macbook Pro and migrated a Time Machine backup of my previous Macbook Pro. I am still keeping the old Macbook Pro in use with all its files. Now I'm facing this problem, when I try to delete a song from my library, no matter from which computer I try to do it, the song just reappears, as soon as the library updates, I guess. I tried deleting it from the new Macbook where the actual file is, and it doesn't work. I tried deleting it from the old Macbook, where the song is shown as an available download but it just reappears after a while. This happens for both, songs uploaded by me and songs from apple music.

Deleting songs from my library only works if I delete them from my iPhone, I can't believe that this is the way for managing my music library, I can only delete songs from a device where I can't edit anything about them. Also I noticed that any changes I make to the songs info doesn't sync across all the devices. I'm used to writing notes in the comment section of songs to sort them in smart playlists according to these notes, but apparently all songs are uneditable once they're uploaded to the cloud, songs from apple music are also uneditable.

I deauthorized all computers and reauthorized both macbooks trying to solve this, but with no positive result.

Any help is greatly appreciated, as I'm also facing the eternal problem of duplicated songs, duplicated songs that I CAN'T DELETE!