https://www.cell.com/joule/pdf/S2542-4351(19)30354-X.pdf
Basically we need 1W/m^2 of cooling for the earth, so if you could get a radiative cooling device with 100W/m^2 you'd need to cover about 1% of Earth's area
so the math works out even better than it seems...?
https://en.wikipedia.org/wiki/Daisyworld
The argument (and the related Gaia hypothesis) has some important and subtle connections to the facts of climate change. Though even if it's correct, and the biosphere will tend to naturally reassert homeostasis, there's no guarantee we'll enjoy living through it.
So we'd only have to paint 1/80 of the Earth. That's ~6.4mln km2, or 2/3 the area of the USA. Still a lot, but not impossible.
I'm sure paint manufacturing scales better than li-ion batteries, and those more than doubled in production volume over the last decade.