Apple Music

I am in the process of moving from my old MacBook Pro running Mojave to a new MacBook Air (M2, 1T). I keep all my music physically on my computer (backups to cloud and external HD) and want to keep it that way. Somehow, though, when I migrated my iTunes library to Apple Music, suddenly all the links to my actual files have disappeared, to be replaced by "Matched" or "Duplicate".

I find that I can still play the songs even with wifi disconnected. Still, I spend long periods off-grid, so this worries me. Are the links to my actual files still preserved somewhere? Will changes I make to song information (comments field, for instance) still be updated to those files?