Moving a Plex server installation to a completely different computer architecture is not officially supported and will always come with some losses.
That article https://support.plex.tv/articles/201539237-backing-up-plex-media-server-data/ only covers moving between machines with identical architectures/operating systems.
The folder path looks differently on Linux than on Windows.
e.g. D:\Movies\My Awesome Movie (2021)\My Awesome Movie (2021) - 1080p.mkv
QNAP NAS’s run Linux.
e.g. /volumes/share1/Movies/My Awesome Movie (2021)/My Awesome Movie (2021) - 1080p.mkv
While Plex can use their unique universal “metadata ID” for movies, to reference them in playlists, for music it has to use the file path and filenames.
And since that file path has changed, your playlists are now pointing to music files which are no longer present under their previous folder locations.
That’s why your playlists still work for movies but not for music.
If you still have the old database copy, you can try to change all the old Windows folder paths to their Linux counterparts, as described in here.
This is strictly unsupported, though.
