Why is there a difference with the materials?

I imported the voxel (.glb) model to three.js editor and the material is applied just perfect, I don’t see any stairs

But when I import the same model on my stage, I see a ladder

What is interesting: if I change Envrionment to modelviewer in the editor, then I see a ladder
But if it costs EQUIRECT, then everything is perfect

How and where can I put this EQUIRECT in my scene and what is it?

You usually want to load a HDR environment map (e.g. via RGBELoader or EXRLoader) and then assign it to Scene.environment. Check out how the basic GLTFLoader example does this if you need a code snippet: three.js webgl - GLTFloader

Please explain how the editor imports objects?
That is why there is a difference between importing into the scene and importing the same .glb into the editor

The editor does not import glTF asset differently like in the example. Below code snippet is the actual import logic:

The usage of DRACOLoader is not mandatory. You only need it when your asset is compressed.