I appreciate the “Apple Recommended” reply. Yet, I feel the need to restate (some of) it, as it’s too “terse”. Assumes too much knowledge on the part of the questioner.
So, I may be mistaken, but the basic fact to know is that the AppleTV is, basically, a ‘middle man’. It takes data which it receives from outside your home, does things with that data, and sends it along to your TV/Display. Just like you cannot simply connect an AppleTV unit to a regular TV and expect to get a picture, you can’t hook an AppleTV up to any monitor, and expect to get a picture UNLESS your AppleTV is ALREADY connected to the internet. To do THAT you have to connect the AppleTV to your modem/route via either an Ethernet Cable or WiFi. So, first connect the AppleTV to the internet (WiFi or Ethernet) and then … according the the Apple Recommended Post … you’ll get AppleTV TV.
I’d note, for the record, as it were, that I have a Mac Studio and an Apple Studio Monitor, and have (one of) my AppleTV’s plugged into the MacStudio with a HDMI cable. Consequently, there is no option to “Screen Mirror” to THIS AppleTV, nor should there be. I … DO … get the option to Screen Mirror to my iPad and the two other WiFi Apple TVs in the house.