I recently added a new page to Beetle for displaying playlists. It looks as follow:
It relies on the beet playlist plugin which provides a easy way to query the playlist tracks from the web API of Beet. The only problem is that this plugin do not allow to list the available playlists, so the index page for playlists requires that the playlist list is provided in the configuration file (see details on gitlab).
I look forward to finding a solution to gather the playlist list automatically.