> Is the color real if it has wildly increased saturation?

It might be more accurate to say that the color is not typically that noticeable by the human eye. It's "real" in the sense that it exists even though we can't perceive it without help, like infrared light, or the sound made by black holes.

This is particularly true if you're looking at pictures of nebulas. The hydrogen alpha light is in the infrared and for humans is color mapped to red.

Cameras are sold with the capability of capturing the hydrogen alpha light. Like the Nikon 810A which is a Nikon 810 but with the IR filter removed.

Agree the saturation is pushed to the point of absurdity in the moon image. Doesn't look like a 'Real' Photo anymore and thus looses it's impact/gravity.