Plex uses “album art”, not “song art”.
i.e. if for some reason all tracks in your library are assigned to the same album, they will appear with this album’s cover art.
There are no songs in Plex which are not assigned to an album, nor without an artist.
If you have tried to achieve that anyway (with some trickery), it could explain your troubles.
I’d verify the folder structure where your music is stored.
If you’ve found that all your music were assigned to “Various Artists”, and you’ve subsequently renamed that “artist” to something else, you are in quite a mess.
See this thread: Music Organization Questions - #6 by OttoKerner
