In Blender 2.91.0 I see the so called Material Preview mode which allows what you're looking for.
There I have the option to use the built in HDRI's or installing my own one by conveniently using the little gear icon on that pop-up window.
There are just three things you need to get such result:
A studio lighting HDRI (like this one shipped with Blender)
Shiny metallic material (Metalness=1, Roughness=0.2)
Transparent background (RenderTab > Film > Transparent)
Rotate the HDRI to your needs, and add white background through compositor :).
It's simple. Just use an Image Texture (your HDRI) for the object's material and connect it through an emission Shader so it emits light instead of being prone to shadows:
From inside the sphere, you can see the HDRI as you would as if it was connected through a World Shader:
If you are using a mesh for the "skybox", all you need to do is make the material visible to camera, but transparent for all other rays. A light path node is used as mix factor in a mix shader node for this.
Then use a normal environment texture in the world.
If you have a real skybox texture then use it on the world as enviroment along with ...
This is possible in EEVEE and Cycles without compositing by using the Light Path Node>is Camera Ray output.
A node setup like below will allow you to do just what you are asking:
This produces the following result in the EEVEE viewport:
Notice that the background rotates, but the lighting does not.