You are correct that according to the law of conservation of energy, the energy stored in a battery is equal to the mass of the battery multiplied by the square of the speed of light. However, the difference in mass due to the difference in energy stored in a fully charged vs uncharged battery would be extremely small and would not be measurable with current technology. The difference would be on the order of micrograms or less. Additionally, the energy stored in a battery is not directly proportional to its weight, but rather to the amount of chemical energy stored in the materials inside the battery. As the battery charges and discharges, the chemical reactions inside the battery are what cause the changes in energy, not changes in the battery's mass.