Just a bit more background so you can make relevant comparisons.
I have three 4K, three 4, and one 3 (plus four phones and four iPads) on my home network, all same SSID and connected to same iTunes library. Technically, they’re all on WiFi though I do have one 4K (not the one in question) connected by an Ethernet cable to a range extender. I’m not sure how you'd regard that.
Only one of the 4’s shows on my phone and iPad. Upon further review, both of those devices were brought into close proximity with the offending Apple TV which I believe is the root cause of the pairing. I can repeat this root caused pairing and hence the Apple TV as an audio source by bringing an iPhone or iPad close to the Apple TV.
I removed the iPhone and iPad using the physical remote of the Apple TV. I no longer see Apple TV as an audio source.