How to remotely & automatically switch a Mac's audio output device

I have a Mac (running Catalina) dedicated as a media server, running Plex and Spotify. I'd like to be able, from my Mac laptop, to simply click something and switch the remote Mac's audio output setting from its internal speakers to 'Bat Cave', my gen 4 Apple TV. Any thoughts about how to accomplish this? I'm more at home with Unix shell scripting than with AppleScript or Automator, but any solution, including hybrid, would be great.