Probably better than a huge lump of vibrating plastic plummeting out of the sky at them

It's most likely that the drone that crashed was similar in size to the type of bird that was spooked (Mavic Mini to Mavic Pro range; maybe a Phantom at most). Anyone flying a larger drone (Inspire and up) would have a serious license and familiarity with permits, therefore unlikely to be called "illegal".

I'm guessing it either fell after colliding with a bird or was flying low enough with sensors off and clipped the ground.

Thunderstorms have been happening with some predictability since before birds even evolved. A buzzing, hovering, and erratically moving clanking mechanical thing is extremely novel.

Which of those two would the birds have a genetically and socially built-in way to cope and survive through?

Thunderstorms are likely rare in this location. Most of coastal California only experiences such storms less than once a year, depending on when they begin nesting any rain at all may not be common, as typically they is little rain from April to October.

Wild animals either shelter from thunderstorm, or they learn from each other differet behaviours (like making herd close-knit) to pull through.