Also having this issue. Also unable to right click a song or album (functions much like the three dots). Also tried various troubleshooting steps including clearing all data and installing from both website and Windows Store.
However, I did find that if you right click or open the playlist you're trying to add it to, then go back to the song, all methods of adding to and managing that playlist are now available, until you completely quit the app. Then you have to work around it all over again.