migration: Remove deprecated New*DB methods
Created by: efritz
Following up from https://github.com/sourcegraph/sourcegraph/pull/28804.
IMPORTANT: Do not merge this until the migrator has been put in place in Cloud and managed instances, the k8s, docker-compose, and pure docker deployment instructions have been updated, and we have backwards compatibility checks running in CI. Once the migrator exists in deploy-sourcegraph, we should have the cluster-test.sh CI check pass and be able to merge this effort.