Palette Filter and Pixelate combined
This is just two shaders combined, resulting in the background in my pic.
Here are the projects separately
https://godotshaders.com/shader/palette-filter-for-3d-and-2d/
https://godotshaders.com/shader/pixelate/
Shader code
shader_type canvas_item;
uniform bool flip ;
uniform sampler2D gradient : hint_black; // It can be whatever palette you want
uniform int amount = 40;
void fragment(){
vec2 grid_uv = round(UV * float(amount)) / float(amount);
vec4 col = texture(TEXTURE,grid_uv);
float lum = dot(col.rgb,vec3(0.2126,0.7152,0.0722)); // luminance
col = texture(gradient,vec2(abs(float(flip) - lum),0));
COLOR = col;
}