First - I would reboot your Mac AND your iphone. When I say reboot your iphone - I mean push volume up (then release) then volume down (then release) and hold the button down on the right side until you see the Apple Logo.
With both devices rebooted. Put your phone in landscape mode (on its side horizontally). Then open Facetime and see if the camera appears. You can click on Video menu at the top of Facetime and see if unchecking automatic camera select on/off does anything.
Otherwise I would:
I would plug your iphone into your Mac using a USB cable. It should then show up in Finder (the little blue/white smiley face). Your see something like "Your Name's Iphone" that way you can verify that it is connected and your mac see's it. Then open Facetime and see if the camera image appears.
Again for this to work your Mac and your iphone should be on the latest release of software. I am running Mac Sequoia 15.2 and my iphone is an Iphone 15 Pro running IOS 18.2. If your not sure your up to date, on your Mac, click Settings, Software update. On your iphone, Goto Settings, General, Software Update. the other thing is that you must be using the same Apple ID on BOTH devices. So if your apple ID is: johnjones@gmail.com you have to use that same account on BOTH your Mac and iphone. They cannot be different or it wont connect.
GoodLuck.
Here is a link that also might help you if you havent seen it yet:
Continuity Camera: Use iPhone as a webcam for Mac - Apple Support