Antennapod, hands down. It's the best podcast app I've ever used, period. Even proprietary options don't come close.

I used to use AntennaPod a few years ago, not sure what it's like now but it looks to still be updated. Nice app as it has built-in search, etc. rather than just taking RSS feeds.

AntennaPod and Podverse are both really good.

AntennaPod is a good one. Personally I use podcastaddict solely because it has casting and I put podcasts on my TV.

Podverse! I'm pretty sure it's the only FLOSS app that has implemented all the podcasting 2.0 features. The only thing it's missing is Android Auto :(

Audiobookshelf can handle podcasts as well

I use podcast addict.

I use AntennaPod but don't love it. It can be quite buggy. Podcast length is never correct for example and will reach the end before the podcast has finished.

Antenna pod is great. Can't sync with desktop tho.

I use AntennaPod and it's okay, I love the look but the UX takes some getting used to and I have no clue if it can sync with a desktop client, I guess with Syncthing there probably is a way for almost any app but I doubt that's what you mean!

I just synced with gpoddersync, like two minutes ago!

Yes, you need a NextCloud server, but it's getting easier to set up than ever before, and there are third party hosts available for cheap.

I use podverse and love it. the other foss setup I have used is antennapod and kasts synced with the gpodder plugin for nextcloud, but kasts was kinda buggy so I switched to podverse