Here's the page for preparing for weather:

https://burningman.org/event/preparation/playa-living/weather/

While it mentions rain - once- it mostly talks about the dust storms, nothing about rain turning a dried up lake into a mud pit.

Another page goes into great detail about how to get the alkaline dirt off your stuff. As soon as possible!

https://burningman.org/event/preparation/playa-living/post-playa-tips/

"Your Car
If you drove your car to the playa, wash it as soon as you can after returning home, because the alkaline dust can corrode your electronics, and do damage to your upholstery, plastics, etc. Before you do anything, get an air compressor (or go to the air station at your local gas station) to blow all the dust off your engine. (Unless you really know what you’re doing, don’t spray water on your engine, as it can damage your sensitive electrical components.) Then, put on a pair of goggles, open all the windows, and turn your AC fan on high. Then switch your temperature control from cold to hot on ALL your different vent options, including both recirculating the air and not. This will start to get all the dust out of your vents.

Then wash your car with a splash of white vinegar in the soapy water. Vaccuum the hell out of it with the strongest vaccuum you can find, and then use Armor All on your plastic and leather parts, as it cuts the alkaline playa dust really well.

So you can do all this, or (be lazy like me and) take it to a professional car wash place. In San Francisco, they recognize playafied cars, and take extra steps — and charge you for them — to wash your car thoroughly, usually running it through the machine twice, and applying extra elbow grease to your playafied bits. It’s worth the money."

Having spent a lot of time in the desert, it will always surprise you. Best to have some idea of how it might. There was an episode of that show "Survivor" where one group of contestants, in Australia, decided to make their camp in a dry riverbed. I just shook my head. And wasn't the least bit surprised when their stuff all floated away when the flash flood hit.

UPDATE: here's the situation page: https://burningman.org/event/wetplaya2023/