For Qobuz it stays in your library and is flagged not available. This happens fairly often. It’s not always because the album is withdrawn, sometimes it’s just a new version and the old one is withdrawn. You still have to delete the old version and add the new to the library. Can’t speak for Tidal.
Label indexing only works on items in your library. Albums on streaming but not in your library won’t be browsable this way. This recent post has quite a lot more detail