I think what has been compiled into the Arduino platform for esp32 is the full published driver code however the external api is what is published as esp-camera.h and sensor.h in driver/include. So you can’t see functions declared in the files in sensors/private_include, which is where set_reg_bits is found.
When you include the driver files in your sketch I think you are allowing your code to reference compiled functions in .a files that are part of the platform. You can probably download the esp-camera library from github, rename and modify it and then reference your own alternative library instead of the one in the platform. That would allow you to add extra functionality or correct mistakes in the library. I haven’t tried this yet but if the author of the library doesn’t respond to some of my issues I may try this.