This problem occurred in two different systems I have. A clean slate system that only had Syncplay installed and my main, lived-in system.
I can'd add files to the shared playlist. Neither drag-and-drop, nor right-click, "Add file(s) to bottom of playlist" function. I momentarily see a files browser window pop up when I right-click.
I can add URLs to the playlist and they work as they should. I've setup the media directories and had a different user make the playlist and that works as well.