Why do bright stars often look as if they have tiny rays or points?

Answer: Edges in your eye or camera bend light

Distance stretches tiny dots — Distance is why stars shrink to tiny unresolved dots in our view. It does not add rays or corners by itself, though; those shapes are added later by the optics the light passes through. A faraway point of light simply makes the optical pattern easier to notice.

Moving air pulls the light — Moving air does affect starlight, but it mostly makes stars twinkle and wobble in brightness. The steady little rays in a star shape are not being pulled out by the atmosphere. They form after the light enters your eye, a camera, or a telescope.

Edges in your eye or camera bend light ✓ — A star is so far away that its light reaches us almost like a tiny point. When that point of light passes sharp edges, such as the iris in your eye or the blades in a camera aperture, the light spreads into a pattern called diffraction. Those rays are made by the viewing system, not by pointy stars in space.