That's the whole point - the inertial and gravitational mass of the system is proportional to the total energy of the system; changes in electromagnetic potenti

That's the whole point - the inertial and gravitational mass of the system is proportional to the total energy of the system; changes in electromagnetic potential affect the energy within and thus also the mass as far as inertia or gravity is concerned. The same applies for electrostatic potential and gravitational potential. "Rest mass" is just a form of energy - after all, the rest mass of e.g. a block of lead consists mostly of the rest mass of protons and neutrons inside, but the rest mass of those protons and neutrons does not consist of the rest mass of their components, but mostly of the binding energy between their quarks - so the block of lead weighs as much as (and because of) the stored binding energy.