I work in a manufacturing plant for a large company that has multiple manufacturing plants throughout the country. Ours is the 3rd largest out of 30+, easily one of the most automated, and we have one of the smallest amounts of employees. For every piece of automation, that's 4-5 people that we don't have to have doing manual labor, instead replaced by a single operator who pushes buttons.
This could easily translate to starships. Reference the engineering scenes from TWOK, with the massive numbers of enlisted crewman. We've never seen that many people working in Engineering in any of the TNG films.