There is a discussion here Gravity and electric charges
About electric charges and whether they can emit photons in a gravitational field. The conclusion is that it still isn't known for sure one way or another. Is this really the case that nobody knows the answer yet?
Any movement in the gravitational field (which is always and everywhere present) without the effect of a force is a movement without acceleration. You will confirm this if you subject yourself to a thought experiment. You are floating next to the ISS, but standing still in space. You will immediately be attracted to the earth. And this happens without you feeling even the slightest acceleration.
Since you and any electron are not subject to acceleration (but follow the geodesic path of the change in gravitational potential), an electron will not emit photons.
