The sunburst itself is primarily created in-camera, not added later. It comes from photographing a bright light source with a small aperture (high f-number), which makes the lens diaphragm shape visible as diffraction spikes.

Key factors:

• Stop down the lens: try f/8, f/11, or f/16 for a stronger effect.
• Lens aperture blades matter: the number/shape of the diaphragm blades determines the star pattern. A 9-blade iris can produce an 18-point star.
• It often looks better when the sun is partially blocked by something like buildings, trees, or edges in the scene.

There may still be some post-processing in examples you see—especially to balance bright highlights and dark shadows—but the actual starburst can absolutely be captured in-camera.

To practice, try photographing a small bright light source like a bulb or candle against a darker background and compare your lenses at different apertures.

Safety note: do not look directly at the sun through an optical viewfinder.