GPT-4 is reasonably good at D3 and drawing arcs on a projection (e.g. orthographic) is not that unique, you’ll find examples of it on observable. However I wonder if you broke down the problem into a small enough task. It performs best if you provide a clear but brief problem description with a code snippet that already kind of does what you want (e.g. using straight lines) and then just ask it to modify your code to calculate arcs instead. The combination of clear description + code I found decreases the likelihood of it getting confused about what you’re asking and hallucinate. If you give it a very long-winded request with no code as basis for it then good luck.
I did try the code snippet technique, but unfortunately it got it wrong. For example, I gave it code that drew arcs but didn't follow the shortest great-circle distance, and it gave me several plausible-looking approaches that were completely wrong (e.g. telling ctx.arc to draw counterclockwise, which does the wrong thing because it needs to use projections instead.)
I eventually just asked it to compute coordinates to a point c perpendicular to the midpoint on the great arc between a and b, such that the angle between ab and ac is alpha. I tried for hours, asking it to work out equations and name the mathematical identities it used etc. but it was all gibberish.