The corridor at around 33 minutes that Carter was working in appears to be the same as the Jeffries tubes in Star Trek: The Next Generation (1987) (The Enterprise D).
For such a large and important endeavor, the Prometheus Project seems to have very few people working on it. There are two guards at the entrance on the surface and two others inside the Prometheus itself. The construction of a starship would require thousands of individuals to get it built and working.
Of course, all the construction crew and technicians were likely given the day off to avoid the news crew seeing or overhearing something they shouldn't.
Of course, all the construction crew and technicians were likely given the day off to avoid the news crew seeing or overhearing something they shouldn't.