using iPhone as camera for Quicktime recording

Hi.

I would really like to be able to make videos on my MacBook Pro (2020, M1) using my iPhone 12 Pro Max as the camera.

I connect my iPhone to my laptop, lighting to usb c cable, all good so far.

I open Quicktime Player, start a New Movie Recording, and select my phone there as the camera.

The problem is that I'm getting (and recording) the complete screen, like a screen capture recording, complete with all the overlays and controls and stuff ... I want it to just record what the lens sees, like it would if you were using Epoccam with Zoom or something.

Is there a way to access the camera in my iPhone on my laptop for Quicktime, or any other piece of software where I can record video on my laptop?

I of course know that I could just record the video on my phone, but there are reasons why it would be much better to be making movies directly on my laptop ... it's in a music teaching situation and everything revolves around being able to immediately play back on the larger screen for the student to see. Etc etc ...

Thanks for whatever ideas anyone might have.