Great. I see that most of the time the formula for gravitational potential is noted as -GmM / r . Based on what I said, this formula shows the energy that is needed to bring an object from a radius of infinity down to a radius of r (for example the radius of Earth). Correct?Yes.
That being said, now that I understand that just a difference in potential energy causes time dilation even if g is constant, does this mean that in case of a varying g with height, time dilation should change even stronger over a Δh compared to the same Δh in a constant g? I'm thinking this because the difference between the velocities between emitter and receiver would be larger in case of a varying g with height.