Linux can read, but not safely write HFS+ (the standard macOS filesystem for hard drives).
If I need a partition that both Linux and macOS can write to, I use FAT32 even though FAT32 is nearly obsolete.
In your situation, I’d make an HFS+ backup of the Mac. You need backups of your data anyway! Drive failures and data corruption are a fact of life, and if you don’t have backups, you’re guaranteed to lose your files sooner or later.
Once you have a backup drive containing an HFS+ partition with your Mac files, you can use a USB3 connector to transfer your music files to your Linux computer.