If the earth is such round, then how come we don’t see the shadow of the mount Everest on the moon ?

Just to give a perspective on how tiny Mount Everest is compared to
Earth : Mount Everest is 8850m high and the radius of the earth ~6400km.
It is only 0.1% of the radius of the earth.

But surely it does cast a shadow on the moon no doubt about it, but you just can’t see it.

Shadows cast by the moon on the other hand…

If you took a look at the recent solar eclipse animations by NASA, then you might have noticed the shadows cast by the moon during the eclipse were not circular (like yesteryears – see figure above).

But had an eerie irregular shape to it. Why is that ?

First thing to note is that if you take a circle and project it on a sphere, the shadow is no longer circles, but ellipses. That’s why the image is elongated.

Importantly, the surface of the moon is interesting; It is irregular with lots of mountains and valleys. Hence you will not get a perfect little ellipse when you project it.

Based on whether it is a valley or a peak it would affect the shadow region during an eclipse.

But as
mentioned in a previous post, eclipses on earth are too surreal to be
true
because if the size of the moon were any bigger then you would be
witnessing only perfect elliptic shadows and none of this complex mess.

But if the moon’s valley were any bigger, you might never achieve complete totality.

Amazing Question. Thanks for asking!