I currently use AntennaPod with NextCloud's version of GPodderSync; which is...adequate.
My ultimate solution would be one where a self-hosted app that tracks and download my podcasts, and then proxy them with some sync mechanism to an android app, but keep them as separate shows with artwork and stuff rather than consolidate them into one feed. I could then choose to listen on the self-hosted web interface or the Android app, and they would be kept in sync.
I wanted to follow up here because I became aware of a pretty good solution for this. It's called pine pods and it's an open source self-hosted service that also syncs with GPodder (or Nextcloud's version of it) so it will keep AntennaPod and itself synched.