World Principle Volume Support sun light

As the other person said, the sun is infinitely far away; the default volume is everywhere , so with any non-0 density the sun will be completely blacked out.

What you likely want to do instead is make the density gradually decrease to 0 as it gets to some height - mist and fog in real life doesn't extend infinitely, and only covers "a bit" of an area above the ground, hence why it's still bright on a misty day; people make some interesting pictures of misty places when they go high up. If the mist extended all the way up to space, it'd be pitch black in real life too...

You can easily do this using the map range node; plug the position into a separate XYZ and map the range of the Z. However, doing this in the world shader seems to be incredibly slow (bug?), and just using a massive cube instead yields considerably better performance...

Eevee renders it incorrectly, as it does many other things due to not being a path tracer (e.g. things with alpha blend, glass through glass, colored shadows...). It's just one of the drawbacks of being a faster rasterizer. The lighting from the sun lamp and the world's surface are not affected by any volumes in Eevee.

the sun is infinitely far away. At any density, not zero, the total resistance to light = infinite. Just do not the sun, but the spotlight. Or not the whole world is volumetric, but only a large cube of volume.