Judging by their ships, they have gravity generators which are small enough and have a small enough ratio of energy consumption to energy generation to be used in something like the Millenium Falcon.

Indeed and it’s quite clear that the Falcon has two gravity planes perpendicular to each other: 1. the plane that supports everyone on the main deck (cockpit, crew lounge, etc.) and 2. the gun battery gravity plane at 90 degrees. This is easiest to see in A New Hope during the TIE Fighter battle in the escape from the Death Star. Han and Luke are sitting back-to-back, separated by a short corridor that sits perpendicular to the main deck. I don’t think most people notice this because it’s not obvious.