A ProRaw file might be 12-bit, but that doesn't mean the iPhone 13 Pro Max display is 12-bit by any means. You can view 16-bit images on an iPhone 13 Pro Max but they certainly don't have a 16-bit display. If the display is 8-bit or 10-bit, then a 16-bit file (image or video) will only be displayed using the color depth of the display. That is why you sometimes see color banding on lower color depth displays when viewing files that have a higher color depth. The lower color depth displays still have to be able to display the higher color depth files, else customers would be extremely angry, but they do so with much fewer colors which tends to make the image or video look less vibrant.
There are tricks that help higher color depth files display better on lower color depth displays. For example, a JPEG can only be 8-bit at best. However if you create the JPEG from a 16-bit RAW, TIF, or PNG file and embed DCI P3 (Display P3) color codec inside of it, it will look as though it has a higher color depth when viewed on Apple displays that use DCI P3. You only get 8-bit of color (16.7 million colors), but those can get a lot closer to looking like 16-bit due to clever software. But what you really are getting is still just 8-bit, and placed beside the 16-bit version it will be evident that the 16-bit file is better. So it is a pseudo 16-bit looking image hiding in a smaller 8-bit file.