I am trying to create a heightmap from blender GIS addon. I am pretty sure that i have applied correct nodes for creating a heightmap (following a video) but the shading viewport shows only bright white.
The problem is you're using an emission shader as a material for your mesh (something I missed when looking at your screenshot).
Since it's emitting light there is no shading on the surface of your mesh, and you won't see the structure properly.
The heightmap was already properly applied to your mesh: the surface is formed according to the height data. But it seems you wanted to apply a gradient to the z-axis, so that the top of the mesh would be white, and the lowest part a solid black.
In addition to replacing the Emission shader with a diffuse one (like a Principled BSDF), you need a Texture Coordinate node instead of the Geometry node you used, and connect the Separate XYZ node to its Generated socket, like so:
Now your mesh will show up with improved visibility:
Note that since your mesh already has the geometry of the heightmap (Mount Fuji), you can use different shaders or image textures.