Apple TV won’t connect to iPhone hotspot

What is your model Apple TV? Identify your Apple TV model - Apple Support

What is your model iPhone? Identify your iPhone model - Apple Support

Does your mobile provider allow/support hotspot use?

For iPhone 12 or later, have you tried setting the Maximize Compatibility setting?

If Personal Hotspot is not working on your iPhone or iPad (Wi-Fi + Cellular) - Apple Support

I have the 1st generation Apple TV

If your Apple TV box is black and 3.9 inches (9.9 cm) wide, then it is at least 2nd generation. The 1st generation from 2007 has no practical use in 2022 anymore.

Try connecting not by selecting a network, but by manually entering the credentials through the Other … option.

Else try a hotspot from a different model phone, or better yet Wi-Fi from a regular modem-router-access point.