AirPods Max play my music from turned off Apple TV

I have an Apple TV and connect my AirPods Max for sound (which is great mostly!)

When I put the Max headphones on this morning, they immediately started playing my music. They weren’t connected to my iPad or iPhone, and neither had anything playing. It was from the Apple TV, which was turned off. Confirmed this by checking Now Playing in Music when I turned the Apple TV on. I don’t listen to Music from the TV. How do I stop it from starting up?

The Apple TV is up to date on the current tvOS 16.2 (20K5331f). The AirPods are current on firmware. This issue is intermittent and has happened on older tvOS versions.

Thanks!