Are we talking fully automated ship with no crew? What would be the point of that? that's basically a space probe, and a space probe can be built MUCH smaller than any ship.
Or then not, depending on the state of the art. Warp propulsion systems may be the size-defining factor, meaning that Friendship 1 without crew might not be any smaller than Friendship 1 with crew...
Isn't an automated ship a probe?
Of a crewed one, for that matter. The junior Christopher from "Tomorrow is Yesterday" supposedly commanded a "probe" to Saturn, and it probably wasn't from an Earth-bound console because it was supposed to be the first such probe in the early 21st century, in a universe where crewed interplanetary travel was routine in the 1990s and interstellar uncrewed probes were being sent in 2002.
We don't know much about the Starfleet terminology regarding automated ships, but we do hear some research ones being called "probes", some transport ones being called "robot ships", and some combat and spying ones being called "drones", without much overlap. FWIW.