The scale mapping solution only works if you don't have to look around with your camera, otherwise you will notice the sphere-like background image has been stretched.
A correct way to do this scale is actually changing the Field Of View (or Focal Length in blender) of your camera, for this:
- Select your camera
- In the 3D Viewport: right-click > click "Camera Lens Angle" and drag OR
- In the Properties panel: click the green camera tab > Lens section > change the "Focal Length" field