After upgrading to Catalina, the iTunes is gone and Music app has come.
Launch Music.
File > Import the old iTunes library stored in a folder in external hard drive, by selecting "iTunes Music" or "iTunes" folder.
Now follow the guide lines of saving the music library in external drive, though it is a little different since it is now Catalina.
File > Library > Organize Library > Consolidate the Music library.
Check the folder path of the library in Preference > File.
It is /Users/soh/Music/Music/Media
Exit Music.
Make a folder MusicLibrary in the external drive.
Copy /Users/soh/Music/Music/Media to folder /MusicLibrary/ in the external drive.
Launch Music.
Preferences > File > Change > select /MusicLibrary/Media in external drive
The path is now /Volumes/archive/MusicLibrary/Media
Check the Songs list.
Exit Music.
Remove /Users/soh/Music/Music/Media
Launch Music.
Check the Songs list.