Screen mirroring not working: iPhone to Apple TV

I have read the earlier posts on this issue, with the link(s) of things to do/check … picking up from there:

• My iPhone & Apple TV are each on the latest rev. for each.
• Each device has been restarted and is on.
• They are on the same WiFi network.
• They are literally (physically) next to each other.

I bring up Screen Mirroring on the iPhone. It spins and spins, never listing any devices.

This is in a hotel so I do not have access to the router or it’s settings.

This hotel has NO password on its WiFi.

This is happening on 2 iPhones.

Any suggestions?