I'm afraid the Array modifier needs to be applied before any texture baking.
Or it will only bake the original tile - which is not what you want.
Use Object or UV coordinates for both your textures
the Noise Texture uses Generated coordinates, when it's not
connected to anything
but Generated coordinates change when you apply the Array ...
Well I just figured it out. You can just bake it. super easy
What I did
Assign a material with HDRI environment texture based on object space mapping to your object.
Unwrap your object
go with bake and make sure bake the map you used in your shader i.e used diffuse node then bake diffuse, Emission then emit etc.
Baked image is perfectly projected on your ...