Just handle voltage and gravity the same. The "voltage force" is the electrostatic force, and "static electricity" drives the current in circuitry. Whenever voltage is non-zero, we have a static-electric force upon any electrons in the wires.
One way to understand this is: take a conceptual approach with "alternate mental toolbox," where the Volt isn't defined as a Joule per Coulomb. Instead, define the Joule in terms of Volts and Coulombs.
In that case, any altered energy of the system is proportional to the transport of a small charge Q across a potential-difference V. In other words, moving a small charged object against a potential-hill is the cause of potential energy. Knowing the voltage-pattern in space, we can calculate the PE of any moving charges. This is typically demonstrated by "charging" a parallel plate capacitor: by taking charges from one plate and forcing them against electrostatic repulsion, moving them to the other plate, which injects energy into the capacitor.
But but... what then does "voltage" mean?
In that case, voltage is a mathematical concept called "Potentials." It is not defined in terms of potential energy. Instead, it's the line-integral of the e-field flux. Instead, it is a way to describe e-fields, even if no test-charges are being moved, with no potential energy associated with test-charges. The e-field is a thing alone, and it still exists even when test-charges are all removed. Imagine an e-field hanging in empty space.
We can view fields as being made of thin fibers, "lines of force" or flux lines. But we can also view fields as being made of equipotential planes, like stacked pages of a book. If flux is the group of imaginary lines in an e-field, what are Potentials? They're the imaginary stacked-layers in an e-field. Either approach is valid, and these voltage-membranes are just as "real" and important as lines of force. We habitually describe e-fields in terms of flux lines because they're easy to draw on flat paper, while potential planes are difficult 3D objects. (Note that the flux lines are always perpendicular to the equipotential planes which they penetrate. E.g. flux lines around a charged particle are radial, while equipotential layers around the same particle will appear as nested spheres, like an onion.)
What is voltage? It's a stand-alone concept: "Potentials." Michael Faraday and JC Maxwell made much of this mathematical concept, back when the rest of the physics community shunned and rejected it. After all, fields didn't exist, and proper physicists only believed in Instant Action At A Distance. Faraday birthed the EM-fields concept, but was ignored. Maxwell put it on a firm mathematical foundation, and finally the fields could be considered as genuine physics-entities; strange objects hanging in empty space. The math concept of Potentials or "Voltage," is one approach to describing these entities.
In other words, voltage isn't a joule per coulomb. Voltage instead is one face of e-fields, when no infinitesimal test-charges are present.
PS, not convinced? If not, then ask yourself, can magnetic potential-fields exist in space, even when no test-poles are being moved around to create PE? And, is there still some gravity in the space above the ground, even when no boulders are being lifted (are gravity potential-fields really made out of Joules per Boulder? What if there is no boulder?) The potential-field still is there above the dirt, and the Volts are still hanging in empty space between the capacitor plates. Well, only if you reject the Distant-Action beliefs of the pre-Maxwell physics community, and allow fields to have genuine existence.