I think this is where the operator pattern really shines. By defining a custom resource that contains the cluster configuration, the operator can detect certain types of changes, such as upgrading Postgres to a new major version, and automate that change the same way that you'd do it manually. Of course, if such an operator doesn't already exist, its on you to build it, but with popular databases like Postgres, they are generally already out there in some form. That said, I'm not sure if existing Postgres operators handle your specific example.
I haven't yet seen good documentation on how these K8s databases handle upgrades. Additionally, they all seem very quick to stream from master to create a new node. That is great, for very, very small db's. But a 1TB db would be royal pain to do that with.