Would space-faring vehicles in interstellar space be in pitch darkness, show reflections from the nearest star or be bathed in light completely?

The brightness of the spaceship follows (almost) the inverse square law, meaning twice the distance from the star, the brightness will be a quater.
In the middle of nowhere, but within a galaxy, it would look like in a moonless, and cloudless night, far away from any artificial light source.
It wouldn't be pitchblack, but much too dark to read a newspaper. You would see the stars in the background, and the fuzzy band of the Milky Way. The starship would occult the stars; that way you would see the black silhouette of the starship.

At 630.1-fold the distance of the Earth from the Sun (about 3.65 light-days), it would look like at full moon (derived from apparent magnitudes of full moon and Sun)

But maybe the starship is illuminated artificially.