I asked you to address why light coming from one side of the Moon is "special" compared to light from other parts of the Moon. You didn't do that.
It's special because the light from the side of the moon, traveling in a downwards horizontal direction, is traveling through more atmosphere to reach far off distant observers.
The light from the side of the moon does emit light downwards, not only to the side, you are correct. That is the light we see - the face of the moon.
You also neglect that when we look at the Moon, if it is a sphere, we are looking at light coming from the sides, just not perpendicular to its surface.
We are, and we see light from the side of the moon which are propagating downwards. The rays which are propagating sideways are lost to refraction. Hence, one does not see the side of the moon.
If light from, say, the crater Tycho is bent off in some direction, why is it also bent off in all other directions, thus enabling it to look the same everywhere?
The atmosphere is equally thick at two 3000 mile distant terrestrial points from the moon, hence the moon will be refracted to a similar degree.
The concept of some sort of refractive effect, or whatever you think causes this, becomes entirely ludicrous when light has to be bent in many directions to make this work.
The atmosphere is a gradient in all directions beneath the moon.
How does a photon "decide" whether to be bent towards the UK, or South Africa, or Saudi Arabia?
The thickness of the atmosphere it must pass through to reach the observer decides how much the light is bent.
It could be argued that refraction cannot cause this sort of bending, bringing up the straw in a drinking glass example. But in the straw-drinking-glass example is a small scale experiment. If the rays continued on their modified path over significant distance the image of the straw upon the water would be significantly displaced, and not just centimeters apart as seen in the straw experiment.