The reason the shadow is gray is because light is bouncing off the other surfaces in the environment. The shadowed area isn't receiving direct light, but it is receiving reflected indirect light.

I don't know where you got that idea.

Your logic assumes there's only one light source, no atmospheric dispersion, light is a particle, and everything around the object is non-reflective. And it's moved to a white background, something we know reflects light.

Edit: This sounds bitchier than I intended so I'm adding in: questions are great and I upvoted you for it.

Imagine how shadows on earth would look if our sun was actually a cosmic LED bulb array with 9 bulbs.

https://en.wikipedia.org/wiki/Umbra%2C_penumbra_and_antumbra

Any light source they're using isn't a single beam of photons, it's a cast cone of light. Actually multiple cones because mostly it's LED array lighting.

So there's an (effectively) infinite number of shadows because it's being hit by photons coming from multiple angles, from multiple little light cones.

The shadows form a distributed pattern behind.

There's other factors like scattering within the media the photons travel through (air) as well as refraction.

e: I tried to make it make more sense. Its about understanding that a light sources are cones of light hitting from many angles at once.

On the backdrop you mean? That would be from light refracting off of other places in the background and converging behind the gadget, partially illuminating the shadow.