The energy comes from the Earth’s mass, I think.
Mass is converted to energy by the processes of nuclear fusion and fission. To my knowledge, no RE scientists believe that this is occurring in the Earth's core, or for that matter inside any other non-star bodies that seem to emit a gravitational field (such as the moon, small asteroids, or the lead balls in Cavendish's experiment).
The problem is that you are thinking of energy as something that batteries have in a finite amount, and which is expended as the batteries get used. Not so. Energy is a useful mathematical object for predicting how systems will evolve over time.
In the case of RE gravity, many problems can be solved easily if you define a "gravitational potential energy field" (i.e. every point in space has a number "in" it); objects always move from places with higher energy to lower energy, and the amount of gravitational potential energy they lose has to be converted to something other form of energy, like heat or light or speed.
In the case of FE gravity, you can just define another potential energy field in space, the "UA potential energy field" or something, where "up" gets you into lower potentials than "down".
The "energy" doesn't
make objects fall or the FE accelerate; it just describes the kinematics of how these processes take place.