Welcome!
I'm not completely sure what you're asking. I'm also not sure what I'm looking at. Is that actually a really cool card, like a greeting card? Or is it an illusion created with excellent vector skills? It looks absolutely real, if it's an illusion.
Are the "peak's shadows" the blue and green papers? Or do you mean the gray shadows. Why do you need to rotate the shadows? Do you mean you want to change the imaginary light source, so that the shadows lie somewhere else?
If you mean the gray shadows, I don't know why they can't be separate, and moved or rotated individually. If you use a drop shadow filter to create the shadows, then you can't really separate them. But if you create the gray shadow by making a separate object, you can do anything you want with it.
For example
-- Duplicate the object twice.
-- Slide one of the duplicates over slightly, so that the distance between the edge of the one on top and the edge of the one on the bottom creates the kind of shape you need to be the shadow.
-- Use either Path menu > Difference or Intersection, or whatever is appropriate to achieve the result you need.
-- Color the result gray, and blur it as needed.
-- Since it's a separate object, you can move it around anywhere you need it
After some scrutiny, if this is not a real greeting card, but entirely a 2 dimensional drawing, they have done some magic with the shadows. The shadows are variable, having more blur and less opacity at one end than the other, creating the illusion of paper over paper. At present, Inkscape can only do that with the gradient mesh (no filter at all) (and a ton of skill!). You would use the same technique I described, to create the right shape, and then instead of bluring, fill it with a gradient mesh and adjust the mesh (this is quite time consuming). Or you could do both, gradient mesh and a little blur.
There's another way to create a variable shadow with Inkscape. It's not easy....it seems like a filter could be made to make the variable shadow.... But anyway, using Interpolation, you can make a variable shadow. However, it adds a lot of weight to the file. I use to know a tutorial for it, but I haven't been able to find it lately. If I can remember enough, maybe I can give you steps to do it.
This is somewhat off topic, but I just saw something on tv about a business which creates unique greeting cards, which when you open them, a 3 dimensional object unfolds itself, and pops up off the card. I remember having pop-up books as a child, where when you turn a page, a new thing pops up. This example you showed is something quite similar -- again, if it were a real card.
