So there are cases in which you could consider energy being "stored" somewhere. The canonical example from EM is energy being stored in the EM field itself like in radiation. In this case for classical static gravitation fields, the potential energy has more to due the motion of the orbiting mass and the nature of the force itself being conservative and so it isn't really stored somewhere in that sense. What I mean by that is a mass that moves against that gravitation force will lose motion due to that force (specifically motion with a component away from the planet) and from math you can then calculate that kinetic energy that would be lost from the orbiting body if it were to get a certain distance away from the mass for example. This process is reversible, that is you can trade distance for kinetic energy, which is a familiar situation like that of a ball being thrown straight up in the air, slowing and then stopping at some height, then falling back down. The reversibility of this trade off then allows you to associate an energy, potential energy, with given heights off the ground which makes calculations easier by considering it as a trade off between the motion and these greater distances. This however isn't the case for all forces. For air resistance this isn't the case, so you can't associate air resistance with a potential energy as a counterexample.

There are however cases in which energy is real in a sense and isn't just a convenience, and for the most part this is when that energy is associated with motion (momentum specifically) of something. Also, that something would be localized and thus could be considered being stored somewhere. For some examples, of course kinetic energy, but for EM energy, you could consider it being the momentum carried by photons after QED.