It’s weird because there’s a Sun Disk Color parameter on the Directional Light under the Atmosphere and Cloud section of the details, so you’d think it would be referencing a material and you’d be able to add your own texture there. I looked at the Sky Atmosphere material, however, and there’s no Sun Disk Color there, so I have no idea what material is creating the Sun Disk. If I find it I’ll update.
In my case I was wanting to make the sun look like a moon, so the easiest workaround I could come up with was to apply a moon texture to a plane, scale it up to 300 and then place it in the sky in the approximate location of the sun disk. When you move around the world, it’s offset from the disk by a few cm, however, you can set the Atmosphere Sun Disk Color (on the directional light) to black and it makes the Sun Disk disappear, and now it looks like the light shafts are coming from the moon texture. Good enough for my situation, but not ideal since you’ll have to change the position if you adjust the light’s rotation.