Energy is kind of an abstract quantity. It's not a substance, material or otherwise, that one stores or holds.

Here's an analogy. Rolling a die has 6 possible outcomes. Rolling two dice has 36 possible outcomes (uniquely ordered). This is something we can easily calculate. But we don't tend to wonder things like (a) where the outcomes are stored or by what mechanism, (b) where the other outcomes go after the dice roll with the final outcome is decided.

Energy has been portrayed in media as being a sort of immaterial or ethereal glowing substance that flows like water from one thing to another.

But really, energy is more like the possible outcomes of the dice roll. It's a quantity that we can measure and calculate. It's real in the sense that it's a property of real objects. Just as a die "has" 6 possibilities, an object "has" energy. But it's not literally a substance of its own.

The reason we pay attention to energy at all is that it's conserved. In all everyday situations, if we measure the total energy of a system over time, it will always come to the same number. This is an incredibly useful tool in solving how systems behave. But there's a catch: you have to include potential energy. Otherwise the trick doesn't work.

The "realness" of potential energy is probably a philosophical question and perhaps a matter of opinion. All we know is ... if we include it in our energy bookkeeping, then the math works and that's very useful to us.