Hello, welcome to the club of AntennaPod users @glenk1!
In addition to what @Listener kindly shared:
Continuous playback is currently not available within a podcast, but only on the queue. There is an open feature request for this: Continuous playback if initiated from podcast screen (+ reversed) · Issue #1533 · AntennaPod/AntennaPod · GitHub
However, you can now keep your queue sorted based on podcast title, which will already help for what you want here. You’ll need “Continuous playback” in the settings turned on and you’ll probably want “Keep sorted” (in the queue sorting) enabled as well.
We don’t know how Google Podcasts worked, but it might be (is quite likely) that they had a centralised approach: their server checks constantly for new episodes and once they find one they push it to you. With AntennaPod, it’s your local app that does the checking and processing (e.g. to prevent duplicates arriving in your list). More info: Central and distributed podcast apps – AntennaPod You might want to check the settings » Downloads » Refresh podcasts, to check more often for new podcasts.
You might want to look into your “Automatic download” settings.
As already mentioned by @Listener, you can determine whether you want to display episode covers or podcast covers in the list: Settings » User interface » Use episode cover. There’s also a request to show the podcast title in episode lists: Show podcast title in items of episode lists optionally