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They said they incorporated the height map from the original.

How did they obtain them? Do museums/galleries/owners let scientists or engineers study the layers of paint of the physical paintings?

Yes they let scientists study the layers.

You can create hight maps by casting light from each side of the painting and using the shadows for your hight map calculations.

Edit: this (old) tutorial shows how you can do it yourself: http://zarria.net/nrmphoto/nrmphoto.html

I think a flat bed scanner is great for creating those maps. Just scan your peace 4 times each time rotating it 90 degrees.