First - A good Idea to have a back up of the external drive (and keep a back up copy of the "iTunes Library.itl" iTunes Data from the Mojave somewhere)
then it's pretty strait forward
Copy the "iTunes Library.itl" iTunes Data from Mojave to your Big Sur desktop (can delete later) - Hold the opt key and open the Music.app - you should get a dialog to "Choose Library" choose the "iTunes Library.itl" on the desktop and it should import / Create a new “music library” in the main music folder and import all the playlists, play counts and lyrics etc into the new library "Music Library.musiclibrary"
If you wish to keep the music on the external drive it will work as long as the path has not changed - if not (path change?) you may need to manually point the Music App to the location of the files on the external drive see screen shot of music preferences below.
I have all my music on an external and can share the drive with Lion - Mojave and Big Sur - each mac has a different Library file of its own but shares the same music files (set path in preferences)
Your Artwork will probably be messed up - mine was - but everything else works
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