How do I go about making this shader

I was sending a gif of my project to a friend, then I noted the compression of the gif so I began to wonder how could I possibly make something like a shader or post-processing configuration that would achieve this effect.

Effect in question:

What it currently looks like:

 

The effect you’re looking for is called posterize.
https://github.com/oxysoft/RetroSuite3D

 

also: posterize is a node in Unity's shader graph
https://docs.unity3d.com/Packages/com.unity.shadergraph@6.9/manual/Posterize-Node.html