In addition to using other forms of energy, you can also over provision. Solar panels still work when it’s cloudy. They just don’t produce as much power. And with a grid you can average cloud cover over a large area.

That's why we have an electricity grid, it's not cloudly all the time all across the world, so even if we went full solar I don't see how it'd be problematic.

Use other forms of electricity generation?

Thankfully when it’s cloudy, your peak loads from AC are a lot lower.