I had to read the OP a dozen times, but I think he might be wondering why we see the shadows at all.
The main (only?) time one would not see shadows is when the light source is coming from the same direction as your vision. For example, if the light source is right between your eyes, you’d see almost no shadows at all. And if you would be standing by the sun and looking at the moon, I think you’d also see no shadows at all. But when we look at the moon from the Earth, and the sun is elsewhere in the sky, then the shadows are easy to see.
Yes indeed, I think the OP is under the misconception that the moon is lit up by the earth. It is, but only to a very small degree. Most of the light is coming from the sun.
Hmmm… If I am correct, then there should be very few shadows and features visible during a lunar eclipse. I do know that the moon IS visible during a lunar eclipse, and it is a verydull brown, and it IS being lit up by what reflects from the Earth. But I don’t remember how well any features are visible then.
Okay, I just looked on Google Images for “lunar eclipse” and for “moon”. I think it is safe to say that VERY few features are visible during a lunar eclipse. Basically, there are only two colors: Brighter, for the jagged mountains, and duller, for the flat “seas”. This can easily result from different degrees of reflectivity. But In sunlight, many individual features can be seen because of the shadows made by the sunlight, and all of that is invisible when the earth is the only light source.