To capture any 4K ProRes footage with 128GB 15 Pro you need an external drive, this is presumably because 128GB model has a single memory chip and data write speeds are insufficient.
I might be doing something wrong, but when I tried to set BlackMagic Camera to ProRes Log 4K60 it had no problem recording it. I was even able to apply different free LUT files and export it to photos. It is 1.6Gb for 8 seconds, but did not require an external disk. [1]
Huh, interesting, I just tested it too and does work in Blackmagic camera (iPhone 15 pro 1TB).
I guess it’s only a limitation of the official Camera app while 3rd party apps can do otherwise.