Old iTunes should be automatically converted to the new layout. If not, Option-start Music.app and choose the old iTunes Library.itl as a library. But make a backup before trying so you can revert, if necessary.
I wanted to manually do the conversion to the new layout so read on if you want to do it the hard way...:
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Old iTunes folder to Catalina or Big Sur Music.app
I have tested how to best import an old iTunes folder to the Music.app on a cleanly installed Big Sur (Catalina was the same but I skipped it). My current "iTunes" folder in Mojave was created 2006 (15 GB folder containing 1800 songs).
With my setup the Music.app could successfully parse the old “iTunes Library.itl” and convert it to the new “Music Library.musiclibrary”.
In that process the Music.app wanted to create a new mainly empty “Music” folder. I want all stuff in the same folder so I manually organised the old iTunes folder to the new Music.app layout:
~/Music/Music/Music Library.musiclibrary
~/Music/Music/Media/Music/[imported and downloaded artists/albums]
~/Music/Music/Media/Automatically Add to Music/ <- created automatically
~/Music/Music/Media/Downloads-Music/ <- created after downloading music
Convert old iTunes folder to the new folder structure:
0. In the old macOS iTunes.app check the song count (View > Show Status Bar) so you can compare it in the new Music.app.
1. Copy the old "iTunes" folder to macOS 11.0 Big Sur ~/Music/ folder and rename it "Music".
2. Option-start macOS 11.0 Big Sur Music.app and choose the old ~/Music/Music/iTunes Library.itl as a library. Music.app prompts to create a new “Music 1” folder. Save it on the Desktop (or where ever because this folder is deleted at step #5).
3. Wait a while for the old library to load (check the song count via View > Show Status Bar).
4. Quit Music.app. Open “Music 1” folder created in step #2 and move "Music Library.musiclibrary" from it to the ~/Music/Music/ folder you renamed in step #1. Delete the temporary “Music 1” folder from the Desktop.
5. Inside ~/Music/Music/ folder create a new "Media" folder, rename the old "iTunes Music" folder to "Music" and move it to "Media" folder you just created.
6. Option-start macOS 11.0 Big Sur Music.app and choose the newly created and moved ~/Music/Music/Music Library.musiclibrary as a library.
7. Open Music.app > Preferences... > Files, click "Reset", "OK" and "Yes" to the alert "Would you like to move and rename the files in your new Media folder to match the "Keep Media folder organized" preference?".
8. Quit Music.app. Inside ~/Music/Music/Media/Music/ folder delete the "Automatically Add to iTunes" and "Automatically Add to Music" folders after verifying they are empty (a new "Automatically Add to Music" was created in step #7 in the upper folder).
9. Inside ~/Music/ folder there might be the following old iTunes files and "Album Artwork", "Mobile Applications" and Previous iTunes Libraries folders that AFAIK serve no purpose anymore and might be deleted:
iTunes Library Extras.itdb
iTunes Library Genius.itdb
iTunes Library.itl
iTunes Library.xml
iTunes Music Library.xml
Album Artwork
Mobile Applications
Previous iTunes Libraries
10. Now you should have all imported songs available in the new Music.app with the new folder structure.
11. Some extra Album Artwork might be downloaded via Music.app > File > Library > Get Album Artwork (apparently works on purchased music and even for some old .mp3 files). Some purchased songs might be downloaded via Music.app > Account > Purchased > Not in My Library > Download.
12. Some purchased songs might be downloaded via Music.app > Account > Purchased > Not in My Library > Download.
13. I grabbed some missing album covers from the old iTunes/Album Artwork/ folder:
There are lots of folders so browsing them is difficult. So put them in the same folder and with GraphicConverter > File... > Browse Flat... > Edit: Select All > press Delete key to move them to Trash (make sure it is empty before doing that) > move all from the Trash to a folder.
Then convert .itc to .png with GraphicConverter > File... > Browse > Right-click: Quick Convert into same Folder as PNG.
Then GraphicConverter > File... > Browse > View > Show all in Slideshow and check if there is anything that might be used for missing album covers (there might be lots of duplicates and low-res covers).
14. Forced some loose songs in the same album in Music.app > select songs that belong to the same album > Song... > Info: edit the album name with some letter and then edit it back to its correct form.