The distortion caused by the changing angle is quite noticeable. Would that be described as astigmatism in the lens?
Astigmatism is something else. That's when a lens is not circularly symmetrical and it can't bring all parts of an object into focus even though they're all at the same distance from the lens. It's a common defect in the human eye. Glasses and contact lenses are ground with two separate focal length parameters, a "spherical" focal length to adjust for simple near and far-sightedness, and a "cylindrical" focal length to correct for astigmatism. The axis of the cylinder is specified with a rotation angle.
The effect here is a shift in
position around the field of view, not a shift in focus. Because you are projecting a sphere onto a flat surface, you have the same problem that mapmakers do. If your field of view is very narrow, e.g., through a telephoto lens, your field of view is such a small section of the sphere that you can pretend that it's totally flat, just as a map of a town or small city can pretend the earth is flat. But as the map covers more of the globe, the non-flatness of the earth becomes harder to ignore. There are many map projections, some more common than others, but none is superior in all cases which is precisely why there are so many.
I don't know the kinds of projections that real lenses use, or if they are even standardized. I do know that wide angle lenses can have at least two very different projections, "normal" and "fisheye".
