That nature paper is garbage. It's imagining a grid that is 100% solar+wind, which no one is proposing building. Changing that to a grid that has 20% nuclear/geothermal would completely change the figures (in that it would dramatically shift the wind/solar ratios).
Also my battery assumptions were missing the fact that the world already has ~5TWh of hydro which can be used as a battery (even when not pumped hydro by releasing only when you need power).
Dams don't double as energy storage in the same way as batteries. Their rate of recharge is limited by precipitation. You can't run a dam turbine in reverse and fill the dam with excess power (you can with pumped hydro, but we have way less than 5 TWh of that). The best you can do is totally shut them off and let them refill. And in reality, dams have to constantly release a minimum amount of water to avoid creating a totally dry riverbed.
Also my battery assumptions were missing the fact that the world already has ~5TWh of hydro which can be used as a battery (even when not pumped hydro by releasing only when you need power).