I am trying to figure out how to draw a shadow from a spherical object onto a non-flat surface. How would I draw the distortion of the shadow onto the surface?
To amplify Billy Kerr's excellent response, if you wanted to set your light source in your illustration other than directly overhead (I can see Billy took, as I do, your initial sketched dashed lines running vertically as your intended shadow edge) you would draw vanishing points from the light source past the edges of your sphere to show the shadow path, and intersect that with your folded planar manifold or ground.
If you wanted a bit more detail, you could add the blurring you see at the edge of shadows, which technically is called "penumbra", and is to do with the geometric relationships between the actual width of your lightsource and the edges of your object (see this wikipedia link for more detail)
I've added penumbra and some basic annotations to my figure to make it clearer: hope this helps.
In case you were curious: all drawn in Affinity Designer, all 2D.