Apple Podcasts app involuntarily mirroring podcasts to nearby AppleTV. Not due to "airplay handoff."
There are other threads on this issue. Here are some. There are more. Going back years, to at least iOS 14.
Podcast automatically Airplay to AppleTV - Apple Community
Apple TV automatically plays audio from i… - Apple Community
Apple Music/Podcast keeps airplaying afte… - Apple Community
My Podcast app automatically plays on my AppleTV, overriding what's already on the TV, and depriving my AirPods of audio. There is no "Auto-Handoff" feature turned on, that is set to never (Settings﹥General﹥AirPlay & Handoff﹥Automatically AirPlay to TVs﹥Never.)
It just happens intermittently, in an automatic and quirky fashion.
Moreover, once it's mirrored, it's hard to pull the stream back to the phone. The screen for the Podcast app changes and looks different, and all the output sources are AppleTVs, and the Airpod destination is no longer there. I have never deliberately used or set up this kind of Apple TV mirroring.
Every other thread I have read on this issue, back to iOS version 14, looks like it was answered by an LLM with a canned answer that does not actually solve the problem. Seriously the apple responses are resembling the worthlessly verbose, robotic-looking answers you can read from "experts" in the Microsoft answer community.
There are tons of "Me Too" votes on this. Do human reps even read this anymore? Probably not.
iPhone 5, iOS 10