I have basically gone this whole entire setup just to get synchronization on AntennaPod and my phone/devices. Is it worth it? Not really as you can do the same with exporting the backup the official AntennaPod to another phone or use an OPML file to do the same for other podcast clients, but its a fun project.
Now that we have Nextcloud up and running now we can install the GPodder Sync app.
After much research and trial and error I have found the gpodder implementation to be very terrible. The only known way to get synchronization across devices is to setup a Nextcloud server and install the plugin/addin gpodder. The other ways that I have tested but could not get any to work due to broken links and or not enough information are with micro-gpodder-server and gpodder2go. Both failed miserably.
The official link/website and how-to from gpodder.net called mygpodder has a broken link and requires various weird ways to get it to work using sqlite3, cargo, npm, etc. The cargo program is run in .exe making me think they have this running on windows and not on Linux.