The media folder is whatever is listed under Music > Preferences > Files.
Reorganise files in the folder "Media" is really a legacy from iTunes. It something you can set if it isn't set, but if the option is greyed out then it is already set. Back in iTunes it would music in a separate subfolder of the media folder in the same that Movies, Podcasts, TV Shows, etc. have always had their own subfolders. Back in the day artist folders would, by default, go into the main media folder. Reorganise... improved the folder layout. Now that Music only deals with Music it would be better if Apple included an option to undo it. If you'd like your artist folders to live one level higher use a text editor to edit the hidden file .Media Preferences.plist in your media folder, changing the line:
<integer>1</integer>
to:
<integer>0</integer>
The turn Keep organised off and back on again to refresh the layout.
If the tracks are marked as part of a compilation then they go to <Media Folder>[/Music]/Compilations rather than <Media Folder[/Music]/<Album Artist>. Often anthologies of a single artist's or band's works, e.g. Greatest Hits albums, will be classed as a compilation whereas this option is, in my opinion, better reserved for albums where each track is by a different artist.
You can use the use the Automatically Add to Music folder in the media folder to merge in new content and have it move to the right place.
And yes, you can delete ~/Music/Music if you're sure there is nothing left in there that you need.
Your library is currently one level higher than Catalina would use by default, but if it is working for you now I'd probably stop there.
tt2