No, when standing on the Moon, Earth does not shine as much as the Moon does in Earth's night sky. The Moon appears bright in our sky because it reflects sunlight back to Earth. However, Earth seen from the Moon would not appear as bright.
The brightness of an object in the night sky is determined by various factors, including its size, distance, and reflective properties. The Moon is relatively close to Earth and has a relatively large size compared to the other objects in the night sky, which makes it appear bright to us. It reflects a significant amount of sunlight towards Earth, illuminating its surface and making it visible from our perspective.
When standing on the Moon and looking back at Earth, the view would be different. From the lunar surface, Earth would appear as a shining, but relatively small, blue and white orb in the sky. It would not be as bright as the Moon appears from Earth since the Moon's surface reflects sunlight more efficiently than Earth's atmosphere and clouds do. The brightness of Earth would also be influenced by factors such as the angle of the Sun, Earth's phase, and atmospheric conditions.
So, while Earth would still be visible and shine in the lunar sky, it would not have the same level of brightness as the Moon has in Earth's night sky.