The problem with solar is that the sun doesn’t shine overnight.

Big if true. Winds tend to be stronger at night though.

if you’re relying a lot on solar, you need to build a big-ass battery that you charge during the day and use at night.

Or pumped hydro, compressed gas, molten salt, green hydrogen, etc.

Nuclear is good for baseline power

Base load. See here: https://cleantechnica.com/2022/06/28/we-dont-need-base-load-power/