The Apple TV may disappear from the devices list in iTunes -- particularly when connected wirelessly -- or not appear at all.

The only devices I've authorized for iTunes in the Cloud are my iPhone and my Mac, and my iTunes account settings confirm this. So is iTunes just messing up and displaying stuff that isn't mine?

If you're running macOS 10.15 Catalina or later, it will appear alongside your removable devices ... may not "see" your iPhone until you've done this, so it's the first thing you should check if your ...