Thanks for your reply. Basically migration assist copied the iTunes folder from my MacBook Pro running High Sierra to the desktop of my iMac running Big Sur. It looks like these are the instructions I would take:
macOS 10.15 Catalina and later
The same basic approach as above will work for moving a library from one Catalina/Big Sur system to another. If moving an iTunes library from an older version of OS X/macOS to Catalina or Big Sur then it will be best to start with the library in the portable shape. You can then option-start-Music to access the iTunes Library.itl file and migrate it into Music. You can repeat with TV. If you've done this already, but Music says that original files cannot be found either revisit the migration or try FixLinks - an AppleScript to repair broken links in Music - Apple Community.
The default location for a Music library in Catalina and later is ~/Music/Music with the media files consolidated into ~/Music/Music/Media. After importing your iTunes library you may want to copy your active Music Library.musiclibrary file into ~/Music/Music replacing any older copy there, then use Music > Preferences > Files to reset the media folder path, and File > Library > Organize Library > Consolidate Files to bring all the music into media folder. You can then remove the originals from the old iTunes Media folder. Repeat with TV as appropriate. Alternatively you could create the nested layout of library folder and media folder on an external drive.
So I would use the import the iTunes Library.itl to ~/Music/Music and then import the songs from the iTunes Media music folder to ~/Music/Music/Media?
What will this also maintain the play list structure for iTunes?