maybe the files are read-only. Idk if that actually affects things, but just check it. And don't forget to replace the files to another directory and than re-move it again.
No they are not read-only. I don't think MusicBee allows you to edit tags if they are read-only.
Maybe my only option is to split the tracks separately. That would be annoying though because then I would have the album twice in my library unless I moved the single FLAC album out of my music folder.
foobar2000 will show the recently played, the last played date in settings, and play count in settings of a single FLAC album. In foobar2000 you just drop the cuesheet into the music library to split the album. It then shows all the tracks individually with their own settings.