I can think of two ways to go about this:
1) Zoom lets you share the iPhone or iPad screen in a call. This can be done either with the cable or via Airplay. I often use this with my iPad, so I can write with Apple Pencil when teaching remotely. It works beautifully.
With the cable, it ensures the device is powered too. With Airplay it works much like, well, Airplay. This should show you just the video and not the interface elements of the iPhone.
One little caveat: in Monterey, in order to use an iPhone or iPad like this using Zoom’s Airplay server, you need to turn off the Airplay server built into macOS itself. Go to System Preferences-Sharing and uncheck “Airplay Receiver”.
2) There exists software that will let you use an iPhone or iPad camera as just another camera connected to your mac, but it is not free. I have not used it. Camo, Epoccam seem to do this.
In this case you would only need to select the camera from video popup menu in Zoom (next to the Dhow Video button), and you can easily alternate between the built-in camera and the iPhone one.