benefit of google podcasts compared to antennapod is that with google podcasts I can start a podcast on one device and later continue where I left off on another device (e.g. listen on mobile then switch to desktop).
I don't use this functionality myself and can't vouch for it, but have you looked into the synchronization options? It seems as if it should be possible. They support self-hosting as well. [0]
[0] https://antennapod.org/documentation/general/synchronization