What specific condition must be met for the sky to be considered truly dark for observing the faintest celestial objects?

Answer

The Sun must reach 18 degrees below the horizon (end of Astronomical Twilight)

Astronomical Twilight ends when the Sun has sunk 18 degrees below the horizon, at which point residual atmospheric scattering is no longer significant enough to interfere with viewing the faintest celestial objects.

What specific condition must be met for the sky to be considered truly dark for observing the faintest celestial objects?
lightskyatmospheresunsettwilight