Interesting article about it:

Archive: https://archive.ph/4EURk

https://www.forbes.com/sites/startswithabang/2018/09/22/ask-ethan-why-arent-rays-of-sunshine-parallel/

You might suspect that clouds are like prisms or lenses, diverging or refracting the light beams and causing them to spread out. But that's not actually the case; the clouds themselves absorb and re-emit the light pretty evenly in all directions, which is why they're not transparent.

Then goes on to say

It's only where the clouds don't absorb most-or-all of the light that you get the sunbeam effect. As it turns out, these rays actually are, to the best we can measure, truly parallel lines, consistent with the Sun being extremely far away. If you found some rays of sunlight that were directed neither towards you nor away from you, but perpendicular to your line-of-sight, you'd observe completely parallel sunbeams. ... ... ... The reason you have a beam at all is because of the perspective of the surrounding shadows, and our eyes' ability to pick out the relative brightness of direct sunlight against a surrounding backdrop of relative darkness. The reason the rays appear to have a diverging shape is because of perspective, and the fact that these truly parallel rays of light are land closer to us than their point-of-origin, way back at the bottoms of the clouds. The Sun's rays really are parallel, but unless they're coming in perpendicular to you, they won't appear to be so. That's simply what it looks like when you view parallel lines as they recede away from you.

So the part I mentioned about "what's shadowed or blinded" hitting your eye is a main part of it combined with perspective.