It’s pretty common to have a rack of batteries that might serve an isle. The idea of these is that you’d have enough juice for the generator to kick in. You couldn’t run these for longer periods, and even if you could, you’d still have the AC unpowered, which would quickly lead to machines overheating and crashing. Plus the building access controls need powering too. As does lighting, and a whole host of other critical systems. But the AC alone is a far more significant problem than powering the racks. (I’ve worked in places when the AC has failed, it’s not fun. You’d be amazed how much heat those systems can kick out).
In my experience, you have building UPS on one MDU and General supply on the other. Building UPS will power everything until generators spin up, and if the UPS itself dies then you're still powered from general supply
Did lose one building about 20 years ago when the generator didn't start
But then I assume that any services I have which are marked as three-nines or more have to be provided from multiple buildings to avoid that type of single point of failure. The services that need five-nines also take into account loss of a major city, beyond that there's significant disruption though -- especially with internet provision, as it's unclear what internet would be left in a more widespread loss of infrastructure.