Hello Juice-Tin,
The light and shadows are adjusted by the lights that you have implemented in your scene. Think of the post process as putting on sunglasses. Yes, you have tinted the world around you, and things will appear differently but they are not directly affecting what is already there. You have added a filter that is calculated on a pass after everything else.
I would suggest looking into manipulating the lights and the shadows they cast in conjunction with the Post Process volume in order to achieve what you are looking for.
Here is a bit of documentation on stylized rendering, Post Processing, and a Cel Shader to help you out.