Add a skylight with bounces. You have to adjust it to dim at night, and bounce more light during daytime.
The athmosphere has basically next to nothing to do with lighting.
On earth starlight intensity doesn’t really affect athmosphere coloring all that much. The full moon on the other hand does. If you are trying to replicate this you need a secondary light, set the the proper orientation/light value.
Keep in mind that the additional light can be made to Not affect the athmosphere (so that you don’t get a red hue when the moon sets).
Always disable the moon light completely if the sun is up - you never want to have 2 directional lights interact…