I've been using iCatcher on ios for years now. It has all the things you mention...

digikata on April 20, 2021 | parent | context | favorite | on: Spotify is killing the open podcast ecosystem (202...

I've been using iCatcher on ios for years now. It has all the things you mention but also a nice set of sorting logic to choose from as well as other per-podcast options like prioritization and number of episodes to download/display etc.