I did the switch some times ago and I love AntennaPod.
Still, I did not manage to have synchronization with a desktop service, and I miss that from Google Podcast.
Also AntennaPod seems to be worse than Google Podcast at Bluetooth connections going into standby during conversational pauses creating jilted cutoffs.
I have not experienced that, but have you tried the Skip silence in audio feature? It does a good job removing pauses in audio which would hopefully solve the problem you are experiencing.
I'm typically looking to entertain myself with a podcast and skipping silence would be like cutting parts of scenes in a movie because "nothing is happening".
It's probably more of an issue with the cheap Bluetooth devices I've tried to use.
Some people don't mind watching syndicated reruns of TV sitcoms that have been sped up to provide more time for commercial breaks. I find that it ruins the experience for me. Conversations have natural pauses and cutting them out in a podcast similarly ruins the experience for me. Google podcasts has this feature and I intentionally don't use the feature.
I don't use sync but it has an option for "cloud sync" in the settings, "gpodder.net" and "gpoddersync" seem to be the only two options but maybe one of those will work.