Why is my MacBook Pro not connecting to Apple TV via AirPlay?

My iPhone casts to my Apple TV without difficulty. My MacBook Pro (M1 Max; Sequoia 15.2) shows my AppleTV in the Screen Mirroring menu and will open the Apple TV and show "Choose this Apple TV…" but then "Could not connect to…"

I've updated MacOS a couple of times since I last tried to cast the laptop screen to my Apple TV. My network setup has not changed, and I've not had difficulty connecting this laptop on this network to this Apple TV on this network in the past---lots of times.

I don't recall installing any new apps or processes that should have any bering on the issue. What could be responsible for this failure?

[Re-Titled by Moderator]