Draw a procedurally-generated palette-indexed texture using a shader in Godot.

byte.gdshader

//Uses a byte retrieval function to treat a texture like a byte array
shader_type canvas_item;
render_mode blend_disabled;
uniform vec4[256] u_palette;
uniform sampler2D u_texture : filter_nearest;
uint byte(uint index, uint width){
	//uint width = uint(textureSize(u_texture, 0).x);
	uint index4th = index >> uint(2);
	return uint(texelFetch(u_texture, ivec2(int(index4th % width), int(index4th / width)), 0)[index % uint(4)] * 255.);
}
void fragment(){
	uvec2 texture_size = uvec2(textureSize(u_texture, 0)),
		real_texture_size = uvec2(texture_size.x << uint(2), texture_size.y),
		position = uvec2(UV * vec2(real_texture_size));
	COLOR = u_palette[byte(uint(position.y * real_texture_size.x + position.x), texture_size.x)];
}

ShadedColorRect.cs

public partial class ShadedColorRect : ColorRect
{
	public const string GodotShaderCode = @"
shader_type canvas_item;
render_mode blend_disabled;
uniform vec4[7] u_palette;
uniform sampler2D u_texture : filter_nearest;
void fragment(){
	vec2 texture_size = vec2(textureSize(u_texture, 0));
	//COLOR = texture(u_texture, (floor(UV * texture_size) + .5) / texture_size);
	COLOR = u_palette[int(texture(u_texture,
			(floor(UV * texture_size) + .5) / texture_size
		)[
			int(UV.x * texture_size.x * 4.) % 4
		] * 255.)];
}
";
	public static readonly ShaderMaterial ShaderMaterial = new ShaderMaterial
	{
		Shader = new Shader { Code = GodotShaderCode, },
	};
	public static readonly ReadOnlyCollection<uint> Rainbow = Array.AsReadOnly(new uint[7]
	{//Just a color test, not a political statement.
		0xFF0000FFu,//Red
		0xFFA500FFu,//Orange
		0xFFFF00FFu,//Yellow
		0x00FF00FFu,//Green
		0x0000FFFFu,//Blue
		0x4B0082FFu,//Indigo
		0x8F00FFFFu,//Violet
	});
	public static byte[] RainbowTexture(ushort width, ushort height = 0)
	{
		if (height < 1)
			height = width;
		byte[] result = new byte[width * height];
		ushort stripe = (ushort)(width / 7);
		byte color = 0;
		for (ushort start = 0; start < width && color < 7; start += stripe, color++)
			for (ushort x = 0; x < stripe && start + x < width; x++)
				result[start + x] = color;
		for (ushort x = (ushort)(stripe * 7); x < width; x++)
			result[x] = 6;
		for (int start = width, y = 1; start < result.Length - 1; start += width, y++)
			Array.Copy(
				sourceArray: result,
				sourceIndex: 0,
				destinationArray: result,
				destinationIndex: start + y,
				length: width - y);
		return result;
	}
	public override void _Ready()
	{
		TextureFilter = TextureFilterEnum.Nearest;
		ushort width = 256, height = 256;
		Size = new Vector2(x: width, y: height);
		Material = ShaderMaterial;
		ShaderMaterial.SetShaderParameter("u_palette", Rainbow.Select(color => new Godot.Color(color)).ToArray());
		ShaderMaterial.SetShaderParameter("u_texture", Godot.ImageTexture.CreateFromImage(Godot.Image.CreateFromData(
			width: width >> 2,
			height: height,
			useMipmaps: false,
			format: Godot.Image.Format.Rgba8,
			data: RainbowTexture(width, height))));
	}
}