Would I be right in thinking that modern ships wouldn't require staff actually in the engine room full time, with the engineering crew working mainly from elsewhere on the ship? Because Star Trek's depiction of the engineering deck looks quite antiquated, like that of an old steamship, still common when TOS first aired.
Modern Nuclear aircraft carriers are steam ships. The manner of producing steam is nuclear fission and not fossil fuels. There are usually only 3 commissioned officers on watch for Engineering and Reactor spaces (one in each Reactor Aux Room (RAR) Enclosed Operating Station (EOS) and 1 in Damage Control Central), while the ship is steaming. Every one else in the RARs and EOSs are a non-commissioned officers. There is also staff in each of the two engine rooms. Civilian ships have a lot less crew than warships because they usually don't respond as front line ships of war.
Our Chief Engineer and Reactor Officer were department heads and were never on Watch in the Engineering or Reactor spaces. They might show up from time to time to observe drills or inspect the spaces for cleanliness. 85 percent of personnel on a Navy ship are enlisted, 15 percent are officers. Officers did no work, and had no specific knowledge to fix anything. Chiefs and petty officers are the subject matter experts and perform and supervise repairs and maintenance with the junior enlisted.