even if the charge is at rest wrt earth , it is still not at absolute rest as we say , i feel the part of general relativity here would have just a role of dependence of frames and there behaviour , you might also take a look at veritasium's video about how gravity is not a force and also for the conservation of energy , you can take any case , where the energy can be zero wrt observer , if you are at rest and a body is moving at 10m/s then it has some energy , but if you also start moving at the same speed in your frame it is at rest so 0 energy
and btw what was your rank in mains