During a New Moon phase as seen from Earth, what is the solar illumination status of the Moon's far side?

It is fully illuminated by the Sun

The term 'dark side' is factually inaccurate because the far side receives just as much sunlight over a full lunar cycle as the near side does. The visibility of sunlight is dependent on the relative geometry of the Sun, Earth, and Moon. When Earth observers see a New Moon, it means the hemisphere facing Earth is unlit because the Sun is behind it from our perspective. In this specific alignment, the far side is oriented directly toward the Sun, receiving maximum solar illumination. Conversely, during a Full Moon observed from Earth, the far side is experiencing its own nighttime while the near side is fully lit.