I’m wondering if creating an atmosphere on the Moon is a good thing.
Is it possible such a transformation might affect Earth’s physical relationship with the Moon, such as altering the Moon’s tidal effect on Earth?
no - as long as the mass stays the same it wouldn't cause any tidal changes, but don't worry. It isn't possible anyway.
Is it possible such a transformation might affect Earths physical relationship with the Moon, such as altering the Moons tidal effect on Earth?
The moon doesn't have enough mass for its gravity to hold an atmosphere down, so I doubt any realists want to try.
But even if we accept for the sake of argument that it could, converting part of the moon to an atmosphere wouldn't change its mass, and so tides would be unaffected. (Whatever stuff we could truck up there would be negligible compared to the overall mass of an entire, well, small planet.)
(Physics is way above my paygrade. Is atmosphere considered mass? Can we still jump 30ft in the moon garden? That's what I would go for. The jumping.)