It sounds like the conclusion we're coming to is that the Enterprise and Galaxy-class in general only need about 800 Starfleet personnel to operate them.
In "Timescape", the USS Hera
was lost with 800 hands. Backstage sources consider her Nebula
class, thus identical in size to Galaxy
, supporting the idea that no more than 800 people are needed - and many of those could be passengers, too. (Onscreen, we don't learn how big the Hera
would have been, however.)
As far as Jennifer Sisko, I though that she was a science division Lieutenant or something.
We never saw her in uniform, so it's hard to tell. It's only in the novelization of "Emissary" that she is identified as a Starfleet officer.