To be clear, I'm speaking about more or less permanent outage. The kind where even if the data center could continue to run indefinitely on diesel, there'd be no point because the customers of those companies have experienced sufficient disruption that shopping for things on the internet is no longer a major part of their lives.
There are any of dozens ways this can happen; suffice to say that Romans in 400 AD also thought their way of life was permanent, and a few hundred years later, there was basically nothing left.
So picture a future archeologist exploring an abandoned data center populated by AWS hosts or Backblaze storage pods or whatever, attempting to recover information from the hardware he finds there. Even assuming all the disks are fully intact, how much chance would he have of recovering anything at all of meaning?
We don't know tons about the Egyptians or Romans or Aztecs from what they left us as their worlds collapsed, but it's possible we know considerably more about them than we'll be leaving for those looking back on us a millennia or two from now.
(And it doesn't even take a catastrophe— look at the effort YC is putting into getting that Alto working, and that's a machine that's just a few decades old!)