Could that be turned into an exterior outlet? Then there are outdoor rated power adapters that could be used. Or look into the floodlight pro or similar to see if those can be mounted into the rectangular box. I don’t have any exterior flood lights cams so hopefully someone with knowledge of those can chime in to see if those will work there.
My house only has one outlet outdoors. My nice neighbor changed the outlet to an Outdoor GFIC outlet then we put a cover over it. I have two V3 cams with power adapters plugged into two smart plugs in it. Cover is similar to this.