What is best practice around backing up the on-prem Storage Gateway VM Appliance

Redeploy is the best practice.

That gateway VM is (mostly) stateless and outside of a few settings, such as local network configuration, all data is stored in AWS:

https://docs.aws.amazon.com/storagegateway/latest/userguide/recover-data-from-gateway.html

Restoring from a backup or a snapshot can be problematic for a number of reasons. First you could end up with 2 gateways that are identical clones, both talking to the service backend claiming to be the authority for the files/volumes/tapes. Second, restoring just the OS will result in the gateway needing to be reset since the cache/upload drives it expected are no longer there or have been replaced with new drives.