Chosen Solution

Is the camera part of the display assembly ($500 as of this writing) or is the part separate?

The camera is not available as a spare from Apple and even the part houses don’t sell it either. You’ll need a new display assembly if the camera has failed. Time to get the needed part MacBook Pro 13" Retina (Late 2016-2017) Display Assembly and heres the guide: MacBook Pro 13" Touch Bar Late 2016 Display Assembly Replacement