Can we ask how much work is done by a conservative force instead of dealing with potential energy? This is certainly a valid question and an equivalent approach.

The work done by a force can be related to the potential energy in this way:

W = -ΔU

Apply this to gravity:

The work done by the force of gravity when an object of mass m is raised a height Δy is:

W = -mgΔy

This applies when g is constant, at least.

The change in potential energy here is:

ΔU = +mgΔy

So, you can do one or the other. For a conservative force, consider the work done by the force or the change in potential energy. Usually we use the potential energy method.