Any cloud engineer worth their salt is going to have their programs be stateless and their data replicated across multiple data centers. Many cloud engineers are not worth their salt, but working in Big Tech, this has been table stakes for 20+ years. There are regular disaster drills, both scheduled and unscheduled, that test what happens when a datacenter disappears. Ideally everything transparently fails over, and most of the time, this is what happens.

The bigger problem is that a war is likely to hit multiple levels of infrastructure at the same time. So the datacenters will come under attack, but so will the fiber cables, and the switching apparatuses, and the power plants, and likely also the humans who maintain it all. High-availability software is usually designed for 1-2 components to fail at once and then to transparently route around them. If large chunks of the infrastructure all disappear at once, you can end up in some very weird cascading failure situations.