The mod has been released. Unfortunately, it is not finished. Maybe someone can make it perfect.
Not just you, the same thing happens to me too. The shadows and everything move but the sky doesn't change at all for me, I did write a comment similar to this in the past but deleted it 'cause I didn't get any replies.The shadows seem to change based on time, but the sky colours and general lighting does not. I assume this is because of TOD Override you get after finishing the game. Is there a way to fix that? (steam legacy_stable)
edit: I wonder if it happens to other people too. It could be a problem with my save