Bayer 4x4 dithering shader for use with Unity's FullscreenRenderPassFeature. This is meant to be plugged into a simple Shader Graph Custom Function node which takes in raw screen position and the URP sample buffer. Also includes 2x2 and 8x8 Bayer matrices in case you want to try those out.

Bayer4x4.hlsl

inline half3 GammaToLinearSpace (half3 sRGB)
{
  // Approximate version from http://chilliant.blogspot.com.au/2012/08/srgb-approximations-for-hlsl.html?m=1
  return sRGB * (sRGB * (sRGB * 0.305306011h + 0.682171111h) + 0.012522878h);
}

inline half3 LinearToGammaSpace (half3 linRGB)
{
  linRGB = max(linRGB, half3(0.h, 0.h, 0.h));
  // An almost-perfect approximation from http://chilliant.blogspot.com.au/2012/08/srgb-approximations-for-hlsl.html?m=1
  return max(1.055h * pow(linRGB, 0.416666667h) - 0.055h, 0.h);
}

float4 Posterize(float4 value, float steps, float bayerValue)
{
  value.rgb = LinearToGammaSpace(value.rgb);
  value = floor(value * steps + bayerValue) / steps;
  value.rgb = GammaToLinearSpace(value.rgb);
  return value;
}

float GetBayer2x2(float2 pixelPosition)
{
  const float bayer_matrix_2x2[2][2] = {
    {  0.00,  1.00 },
    {  0.25,  0.75 },
  };
  return bayer_matrix_2x2[pixelPosition.x % 2][pixelPosition.y % 2];
}

float GetBayer4x4(float2 pixelPosition)
{
  const float bayer_matrix_4x4[4][4] = {
    { 0.0,    0.5,    0.125,  0.625 },
    { 0.75,   0.25,   0.875,  0.375 },
    { 0.1875, 0.6875, 0.0625, 0.5625 },
    { 0.9375, 0.4375, 0.8125, 0.3125 },
  };
  return bayer_matrix_4x4[pixelPosition.x % 4][pixelPosition.y % 4];
}

float GetBayer8x8(float2 pixelPosition)
{
  const float bayer_matrix_8x8[8][8] = {
    { 0.000, 0.500, 0.125, 0.625, 0.03125, 0.53125, 0.15625, 0.65625 },
    { 0.750, 0.250, 0.875, 0.375, 0.78125, 0.28125, 0.90625, 0.40625 },
    { 0.1875, 0.6875, 0.0625, 0.5625, 0.21875, 0.71875, 0.09375, 0.59375 },
    { 0.9375, 0.4375, 0.8125, 0.3125, 0.96875, 0.46875, 0.84375, 0.34375 },
    { 0.015625, 0.515625, 0.140625, 0.640625, 0.046875, 0.546875, 0.171875, 0.671875 },
    { 0.765625, 0.265625, 0.890625, 0.390625, 0.796875, 0.296875, 0.921875, 0.421875 },
    { 0.203125, 0.703125, 0.078125, 0.578125, 0.234375, 0.734375, 0.109375, 0.609375 },
    { 0.953125, 0.453125, 0.828125, 0.328125, 0.984375, 0.484375, 0.859375, 0.359375 },
  };
  return bayer_matrix_8x8[pixelPosition.x % 8][pixelPosition.y % 8];
}

void Bayer4x4_float(float4 PixelPosition, float4 Color, float Steps, float RenderScale, out float4 Result)
{
  PixelPosition.xy *= _ScreenParams.xy * RenderScale;

  float bayerValue = GetBayer4x4(PixelPosition.xy);
  float4 outputBayer = step(bayerValue, Color);

  Color = Posterize(Color, Steps, bayerValue);
  Result = Color;
}

I was searching for Bayer dithering to implement for my custom shader in Unity. Yours helped, thank you!