How does Mirroring Wk on APP

Mirroring from iPhone to TV requires that the TV (or a TV-connected streaming device [read: Apple TV box or Roku]) supports AirPlay receiving. Other local streaming protocols are not supported for Apple’s own apps.

List of AirPlay-enabled smart TVs and third party streaming devices - Apple

Use AirPlay to stream video or mirror the screen of your iPhone or iPad - Apple Support

Alternatively, select reasonably modern smart TVs support the Apple TV app, so that no local streaming is needed. Select TV-connected third party streaming devices support the Apple TV app, so that no local streaming is needed. For best experience (imho), get the Apple TV box to connect to a TV through HDMI, which obviously includes the Apple TV app. I think it is better than what smart TVs offer. Apple TV app vs. Apple TV box - Apple Community

Get the Apple TV app or Apple TV+ app on your smart TV or streaming device - Apple Support

Watch on these smart TVs and third party streaming devices - Apple Support

How to watch Apple TV+ and more - Apple Support

Alternatively, you may be able to use a HDMI adapter with iPhone, if you’re willing to give up phone portability during this type of use. E.g.: USB-C Digital AV Multiport Adapter - Apple