This is mere ray-tracing problem. What we call bright sky is reflections of Sun rays from particles in atmosphere. What we see is reflected light. When Sun is

This is mere ray-tracing problem. What we call bright sky is reflections of Sun rays from particles in atmosphere. What we see is reflected light. When Sun is shadowed by Earth we see only light reflected by distant object, such as Moon. The darkness of the night sky is relative - some rays are here, but our visual system is conditioned for days (reflected light), not nights. The idea that everything should be filled with starts is just wrong. Rays from distant stars were deflected, blocked by particles, etc.