How did you set the exposure time?
You may want to try this -
- Zoom in on the Moon, tap it to decrease the exposure until you can see the details on the lunar surface
- then zoom out agin and take the shot.
I am using an iPhone 15 Pro Max, but the same problem. Without manually adjusting the exposure for the lunar surface the Moon will be terribly overexposed.
Here is recent photo of the Moon taken with my iPhone in full daylight, showing the dark patches on the surface. It is easier for the half moon, the full moon is now very difficult to capture with the iPhone.

The full moon at night, with an exposure reduced by -0.5 ev: I could not reduce the exposure time more, so it is slightly over exposed:
