I've been warming up to switching to GrapheneOS for months. Last month I bought a Pixel 8 (which is the buggiest effing phone I've ever owned, good job Google). I've just been waiting to have the bandwidth.
But with Google sunsetting Google Podcasts, I've decided to make time next week. Podcasts are a MAJOR part of my daily functioning.
If you self host nextcloud, another option is to put the rss feeds for your favorite podcasts into the news app. I listen to all of my podcasts through that.
However... I'd totally be interested in a better self hosted podcast app that allows me to see a record of everything I've listened to, while also allowing me to download the episodes to my phone, lol. That's the only reason I'm stuck on the news app still.
Maybe the gpoddersync-nextcloud app is more your thing? You can use that with all podcastapps that support gpodder sync.
Works with Antennapod on Android and Kasts on KDE/Kubuntu.