The sun is not affecting the lighting of the nebulae, as it is a kind of trick/hardcoded light direction, just to reinforce the volumetric look. But considering the scales, the sun should not affect the lighting of the nebulae
The sun is not baked also because it is supposed to be more local than the background which is very very far away. If you want to fly in that solar system, you should render all planets and the sun in 3D, that should be more convincing.
You can do a quite basic sun using GD too, or simply put an emissive sphere in your scene.
I hope this clarifies things, cheers!