Where is this battery draining code from?

Which I can do, but that way there's no way to track if the problem stems from the communication with gadgetbridge?

Well, hopefully you'll get a stack trace which will point straight to the Android app on the watch, which would help a lot - but as you say you wouldn't see that message if you were then connected to Gadgetbridge (unless you used logcat, or use the new 'remote connection' in the Gadgetbridge app loader).

You could definitely try and enable logging and see what happens - there is even logging in Gadgetbridge itself (or you obviously have Android Studio set up so you could look at logcat to see what's being sent).

I think if you're looking at the Gadgetbridge logcat while using Podcast Addict and you're seeing a bunch of data transferred to the Bangle, that could be a good step to see what's going wrong. If you can isolate the GB(...) message that's being sent, we could try running that in the IDE with debugger;GB(...) and trace through exactly what happens.