I guess this is an interview level question.
1) Drain connections from your instance. Stop taking new connections and let all existing requests timeout. This could be by removing it from a load-balancer or dns. This ensures your litestream backup is "up-to-date".
2) Bring up the new deployment, it restores by litestream. When restore is complete, register it with the load balancer (if you are using one) or dns.
3) Delete the old instance.
Yes... and all I see here is downtime. How do we do this without services failure? With a postgres db, you can spin up and down ec2 instances to your hearts content. Every 1-4 years, you can upgrade your db by using a replica with no down time.
Instance can be process, container or machine.