Can an I phone be connected to studio display

If you mean connected to back up or sync then yes. Just use a lightning to USB-C cable. You Mac will recognize the connection.

Not sure what you are trying to do. Your Studio display is connected to a Mac. You can connect the phone to one of the display ports or one of the Mac ports using a lightning cable to USBC cable. It will then show in the Finder list of components.

Can it display what’s on your phone?

It can if you follow this:

https://support.apple.com/guide/iphone/wirelessly-stream-video-photos-audio-mac-iphd668e80e6/ios

So I need to connect a Mac to my iPhone to for it to work with the studio display?

is there a direct connect from phone to studio display?