g is not constant on the surface of the Earth because the Earth does not have a spherically symmetric density. On top of that, there is the effective gravitational field (g) that changes due to location and the rotation of the Earth.

Here's an example of the deviation of g due to a mountain as an early method to measure the universal gravitational constant (G)

https://www.wired.com/story/you-can-find-the-gravitational-constant-with-string-and-a-mountain/