You would need to create it like any other texture you would want to use in the background.
Here I did it for you. I made it tilable too.
Shift + A > image as planes.
Then put it as your Background (Probably shadless is best option for this).
EDIT: OP wanted it animated.
Ok I will solve it 90% of the way for you.
You will need at least a 4K Texture for this (So I created it for you, 1 small problem, we will get to that shortly).
Here is a link to 4K texture (MODS not sure where I should put this.)
Set it as your environment background.
*If you are using an HDRI you will need to set up the nodes like below so you can see the image of the BG you want but have the lights and reflection of your origianl HDRI.
The problem with the 4K texture is that it needs to be "Spherized" (I think I just made that word up). I didnt look how to do this in Photoshop that is why you see the squares stretched a little in the GIF I provided. I also provided what an HDRI should look like so it is wrapped around the world correctly. I know how to do this in Blender (Panaramic, Equirectangluar) but havent looked how to do it in Photoshop.
If you look at the gif you can see the checker BG change from the OG to the one I made, Its real quick.
Keep in mind the texture will be turning with your camera, not like how it stays static in the viewport. This can be distracting.
This is not a real HDRI this is just what they look like HDRI HAVEN
Or you could just make a huge sphere to cover everything in your scene (might cut off some of your sun lamps) apply the texture to the sphere and make sure you have your lights and camera in the sphere.