Hi again, I’ve figured it out:
The setting change that makes the lockscreen controls disappear isn’t in Antenna Pod, it’s in the phone’s Settings, under Notifications. I don’t need the little green “badge” (if that’s the right word) showing up on the Antenna Pod icon on my phone’s screen when a podcast has been updated, so I switched off notifications for Antenna Pod in the phone’s settings.
Through process of elimination I now know that this is what caused the problem. Why? I don’t know. Is it an Android thing? Or an /e/ thing? I don’t know (yet, but I’ll check in with the /e/ forum).
The good news is, reactivating notifications immediately reactivates the Antenna Pod lockscreen feature.
The bad news: I constantly have a little exclamation point on the Antenna Pod icon. Oh well, I’ll survive it 
I was really glad to get that quick response, ByteHamster, thanks!