Are pulumi stacks backed up?

What exactly do you have in mind? Every version of the state file associated with you stack is stored in your backend - pulumi.com by default, but you can use local disk of cloud storage instead.

We are wondering if pulumi backs up pulumi-hosted stacks.

Yes - all state files for stacks managed by the pulumi.com backend are stored in durable cloud storage (currently S3 - which claims 99.999999999% durability) and cross-region replicated for increased availability in case of catastrophic regional outage.

Great, thanks Luke!