I basically gave up on podcasts on the desktop and only use AntennaPod on my phone. When I’m at my desktop, I have my phone paired with my computer via Bluetooth and play that way. I can pause it on my computer via KDE Connect (GSConnect on GNOME).
Bluetooth audio from phone to desktop works on Fedora Linux quite well. It probably works on other Linux distros too. I’m guessing it might also work on other OSes like Windows and macOS.
KDE Connect is available on Android, iOS, KDE (and can run on other desktops too), GNOME (via the GSConnect extension), Windows, and macOS.
This solves the syncing problem by sidestepping the need for it. My podcast state is always correct and I always have my podcasts with me, even when out and about.
If you’re in Europe, it may be due to the DMA.
https://www.lemonde.fr/en/pixels/article/2024/03/06/digital-markets-act-how-the-way-you-use-google-maps-and-messenger-is-changing_6591969_13.html
Google is one of the “gatekeepers” according to the DMA (Digital Markets Act). The law recently went into effect. It is supposed to lessen the amount of preferential treatment the big tech companies give themselves.
https://en.m.wikipedia.org/wiki/Digital_Markets_Act