The symlinks to your sound library are here:
/Library/Application Support/GarageBand
/Library/Application Support/Logic
If they are broken, then the corresponding folders aren't in their expected location.
To find out where the symlinks were originally pointing to, type in Terminal:
readlink
… + whitespace and drag & drop the symlink from Finder into the Terminal window, press Enter.
You can put the two sound library folders to any location you want, then simply replace the two aforementioned symlinks with fresh ones:
ln -s /path/to/your/new/location/GarageBand/ /Library/Application Support/
ln -s /path/to/your/new/location/Logic/ /Library/Application Support/
Instead of typing the paths, you can again simply drag & drop the source and the destionation folders into the Terminal window.
I, for one, am keeping my sound library on a disk image sparse bundle on a larger partition. The disk image is in my login items to mount the volume automatically, but with the "chflags hidden" flag which makes the disk image volume invisible in Finder, thus out of my way. I can still open it by following the symlinks. Or by cmd-shift-. to see invisible files in Finder.
The best of all, you can also manually relocate any other huge library folders like /Library/Audio/Apple Loops etc.
You can even "outsource" the Logic Pro X.app itself by using the symlink magic! See https://discussions.apple.com/thread/252212720?answerId=254201988022#254201988022
(My Catalina partition is only 64 GB and I wanted to install Xcode on it as well, so I had to make a LOT of free space. In fact, I have then outsourced the Xcode.app with its whopping 33 GB size via symlink, too, haha…)
That all said, you should only proceed with such tricks if you know what you are doing, and after making a backup first. Things can break easily if you're not careful.