Music playing but files are not showing up on HD????

The section on iTunes Media Organization is relevant here. Consolidate Files only affects content outside the currently designated media folder. Turning Keep organized off, applying, then turning it back on, rearranges what is inside the media folder according to the layout value in the .Media Preferences.plist inside the media folder. If that value is 1 everything is moved to a /Music folder inside the media folder. If 0 then the <Artist> folders go directly in the media folder. I would change the media folder to your current iTunes Media folder. Edit the .Media Preferences.plist file to change its value to 0. Then turn Keep organized off, apply, and turn back on. This will bring <Artist> folders up into iTunes Media.

Subsequently you could rename iTunes Media as Media, copy your .musiclibrary package from your system drive into iTunes, option start Music to access the library at <External>/iTunes/Music Library.musiclibrary, close, and rename iTunes as Music, which would fully transform the library to one that runs completely on the external drive and looks like it was created in Music. You may still have some old iTunes cruft to throw away which is covered in the user tip.

tt2

See Managing your Mac media libraries - Apple Community for some general background. The media folder of an iTunes library would normally be set to the iTunes Media folder, with iTunes adding in an additional Music folder to separate music from movies, podcasts, etc. Having set a deeper level folder new content will be going to iTunes Media/Music/Music instead. You can pick iTunes Media as your media folder, then turn Keep Organized off and on again to bring everything into one folder. And if you can restructure things such that you get the new layout of a Music folder that has your .musiclibrary package inside it along with a Media folder that holds all of your music.

tt2

Do you have a subscription to the Apple Music service? Do you get an exclamation mark for a missing file, or just not find the track in the folder you would expect? Does right-click > Show in Finder reveal the actual location?

tt2