You can use any normal DB migration tool. For k8s, I put the app's readiness probe to false, run the migrations and then toggle the probe back to true.
I wonder what happens during blue green or canary deployment?
if your migration changes database schema in a way that affect previous version negatively?
is it even possible to do blue/green deploy if your schema changes radically?
It's fine if you make the changes backwards compatible a version. And in general, any change can be done in a backwards compatible way (although it can be a PITA)
Here are some migration libraries:
Go - https://github.com/golang-migrate/migrate
Node - https://github.com/salsita/node-pg-migrate