While a Carrington event would be catastrophic, it won't be even a generation (80 years) before some capacity to access digital data returns. I'd argue it would be days to months.

Carrington wouldn't wipe out everything, just a lot of things, mostly power supply related, at the consumer level from my understanding, and that would be things that are connected to a sensitive grid. Any laptop or tablet not currently on power would be fine, and their switching power supply would likely be protective (In that it would probably fry first).

I've worked on disaster recovery plans that would survive Carrington, during which I studied extant data centers (which would survive one without missing a beat, because Carrington is a subset of the risks they've mitigated). Some were capable of surviving things like a direct impact of a Cat5 hurricane, 1000 year flood events, had power filtering on a massive scale (their greater concern was malicious actors), multiple redundancies of power sources (last one I reviewed had 5 separate power providers each coming in from a different direction, each capable of running the entire facility, with on-site generation capable of running for a week before needing fuel).

So if data centers like these are already operational, just think about the engineering and planning that started more than 20 years ago (one data center I reviewed had been operational since 2005), and what these same engineers/teams have been looking to mitigate.

Then there's all of us ~~home hoarders~~, self-hosters, and their combined planning and capability. Many of us already run commercial power management (full-isolation UPS), with a variety of storage systems, backups, etc.

Seems to me the greater challenge with disaster is connecting unaffected resources to impacted locations.