I tried to repeat what I did in the first file with the background image but the image does not show up in the second file.
In the first image you can see that you have "equirectangular" as an option, which isn't there in the second image. So I assume you have first Color node set as Environment Texture and the second as an Image Texture.
Click on the Color dropdown and select Environment Texture, then choose your image. That should solve it.