Imagine i connect 4 rigid rods of equal length together in a square. This thing has 4 corners, each with a 90° angle. Going around the whole thing i make one full rotation, so 360°.
Now i replace one of the rods with something else: In case A i just replace it with a stiff spring. That spring is build so that its uncompressed length is the same as the rod it replaces. The new object now has 3 rigid rods at 90° angles, and one spring, with zero potential energy stored in the spring
In case B i replace one of the rods with some kind of linear actuator attached to a generator. Changing the length of that actuator will turn the generator and generate extractable electrical energy.
The rods are as rigid as physical possible, so their internal forces are still mediated by the electromagnetic force.
This device is build far away from a gravitational field in freefall. Now i bring this device closer to a planet (with ordinary schwarzschild geometry). The closer i get the more geometry is distorted. In particular, as the device encloses a finite area, if i parallel transport a vector around it, it does not close back to the 360°, but has some angular deficit. This in turn will in case A compress the spring and in case B compress the actuator which will generate energy in the generator. In case A there is some energy in the spring, in case B i can in principle extract that energy and store it in a capacitor. By varying the load on the generator i can extract as much energy as i want, up to the point where the material strength cannot withstand the force anymore.
(since the device is not a single point a "local observer" is not well defined, but i assume an observer very close to the device)
Extended setup 1
I can place this thing in an elliptical orbit around a black hole, so it oscillates between regions of high curvature and regions of low curvature. During every cycle the actuator is extended and compressed, generating energy every time.
Extended setup 2
I can stand on a planet with no atmosphere and launch this device on a suborbital trajectory. I am expending energy to do this but in principle, the energy extracted by the generator can exceed the energy expended to launch it in the first place. I can also in principle recover the kinetic energy leaving me with a net positive energy.
Where does this energy come from (if it even works)? Would observers agree that the actuator is moving? (for device B)
Since the changing curvature creates material stress which in turn applies a force on the spring (for device A), does the whole device "resists" moving? Or is there no counterforce on the device itself?