Finish Home Setup error (-71160)

I am trying to finish the "Home Setup" on my Apple TV 4K. As directed by the Apple TV software I bring my iPhone 12 close to the Apple TV unit where I get the card which asks me to connect the phone to the Apple TV to finish the Home setup. I click 'Connect' and then nothing happens for a minute or so until I get the "Failed to Connect error (-71160)" message.

Apple TV is up to date with v. 14.2 and is logged in to my iCloud account

iPhone is up to date with 14.2 and is logged in to my iCloud account

I've rebooted both devices and tried several attempts, but always get the same error message.

Any suggestions on what I can do? Beginning to tear my hair out on this, distinctly 'unApple'...