I don’t agree here. There are operators like the one I’m a maintainer of (CloudnativePG) which works directly with Kubernetes, teaching it how to handle Postgres clusters as a coordinated set of instances. Enormous improvements have been done in the last couple of years, and we are particularly focused in working together with storage groups in Kubernetes to handle database workloads, such as for example declarative support for tablespaces and volume snapshots.
I suggest you to read CloudnativePG documentation as well as this article: https://www.cncf.io/blog/2023/09/29/recommended-architecture...
Also watch the video of my talk at last Kubecon in Chicago about handling very large databases.
I hope this helps.