Shutting down Apple Tv

Hi:

it indeed does not have a user “shutdown” per se.

That said, I generally put mine “to sleep” ... probably more out of habit than actual need.

Hold the display button for a few seconds snd then select sleep.

You might find this online user guide helpful too.

https://support.apple.com/en-au/guide/tv/welcome/tvos

should have added, depending on your overall configuration, “sleep” might also “turn off” some or all connected devices too.