Ran into this last night. A baffling oversight in the upgrade.
I did retain the "playlist" (at least by name) that I use for my playlist, and the "now playing" button still took me to the current podcast I had been listening to. Podcasts even play in the order I've assigned in the playlist, but as mentioned by others, the podcasts don't appear in the playlists (the playlist is entirely blank).
It also appears that I am able to sync so that old podcasts are deleted, and new ones are added, and they seem to play correctly. I don't know what will happen if the app crashes, and whether this blind link would persist though.
So playlists seem functional but the blank list is disconcerting. The advice to delete the podcast app is a brute force work around that we shouldn't have to do.