UPnP playlists are stored locally on the app, so they are not transferred automatically to other devices. I assume the logic here (if there is any!) is that different users may want to store their own playlists independently of other users.
If this doesn’t suit you, an alternative would be to create and manage your playlists on your UPnP server. How easy that is will depend on which server you run, but if you do this, they will appear in the Server input on the Naim app and will be available on any device.