It looks like Spotify has changed the way it works with albums. Since the redesign, you could click 'Save' on an album and it would show up in CuteSpotify. Since today, they show up in Albums instead of playlists and nothing appears either in CuteSpotify or the official desktop app.

I don't know what has changed in the API, but I guess it is just a new logic to save music by albums instead of playlists. I like that approach, but it might require some work to reflect this in CuteSpotify