Best answer by John B
Around about v8.0-v8.2, Sonos changed the mobile controller to introduce the 'My Sonos' section. Sonos Playlists and Favorites were removed from the list of music sources and put in 'My Sonos'. In effect, the ability to have favorite Sonos playlists was removed in the mobile controller. The term 'Favorites' was dropped in the mobile controller.
The desktop controller still appears to use the old structures and terminology - Sonos Playlists and Favorites look like they are in music sources, but I suspect that this is just an imperfect view of the mobile structures.
I can save Google Play Music playlists to Favorites in the desktop controller - they then appear under 'Favorites' in the desktop controller, and in a 'Google Play Music Playlists' section of My Sonos in the mobile controller. I would have expected playlists from your music service to be treated similarly.
I am not sure I have made a good job of explaining that, but then it is a bit of a mess, IMO. I have said that on here before, and argued that Sonos Playlists should be in the 'Browse' section of the mobile controller, as a music source. Then you could save favorite playlists (music service or Sonos) to 'My Sonos'. In fact, you could even rename 'My Sonos' as 'Favorites' and sanity would be restored 🙂 .