Rule of Google: if it works, kill it.
I know, I know, using Google apps isn’t the best, but this was a perfectly good Podcast app with all the features you might want.
Apparently they’re moving everything over to YouTube Music, where a lot of the features of Google Podcasts aren’t implemented yet.
I’ve moved over to an app from F-Droid.
I use Audiobookshelf for audiobooks, but apparently it supports Podcasts too. I haven’t tried that feature yet.
It’s a self-hosted system that you run on your own server.