That isnt how it works. The speed of light is the speed of causality; it doesn’t have anything to do with light. Its just the fastest speed at which things can happen. Light, being massless, happens to travel at that speed.
In your scenario, the light beam would just be stretched along its length and the 2D interface on the surface of the moon would just “lag behind” from your POV. But it would lag at the speed of light.
That isnt how it works. The speed of light is the speed of causality; it doesn’t have anything to do with light. Its just the fastest speed at which things can happen. Light, being massless, happens to travel at that speed.
In your scenario, the light beam would just be stretched along its length and the 2D interface on the surface of the moon would just “lag behind” from your POV. But it would lag at the speed of light.