Is there a provider that would cover the customer's damages like interruption of business? There are some insurance companies at least that do similar things.

A SLA would. I would just use multiple backups. One self-hosted on-premise and two off-site. Then the two off-site can have egress costs. Wouldn't matter. The self-hosted one would be the primary one to backup from. And it is going to be solid, usually. For example, a Synology NAS would suffice.

I think nearly all SLAs just give you discounts on the service's bill.

Eg if your service vendor costs you 1000/month and they have a 10-day outage and you lose 10000000, they will credit you 1000 best-case, or maybe 1/3 of that (since it was up most of the month).

> if they fail, they cover damages

Umm, most providers' standard T&Cs exclude liability for indirect or consequential loss following unavailability of their service.

I'm sorry, S3 insures your data in case of loss? How come they don't ask the value of what you're storing then?