Sure. But electrolysis is >70% efficient, so even if the bacterial metabolism is only 30% efficient the end to end efficiency is a factor of 10 higher. You are

Sure. But electrolysis is >70% efficient, so even if the bacterial metabolism is only 30% efficient the end to end efficiency is a factor of 10 higher. You are also going straight to complex proteins, whereas photosynthesis produces just basic hydrocarbons.