CloudNativePG supports Kubernetes Local Storage as one of its main features [0]

  Persistent volume management, including:
    Support for Local Persistent Volumes with PVC templates.
    Reuse of Persistent Volumes storage in Pods.
    Separate volumes for WAL files and tablespaces.

Chapter Temporary PostgreSQL Cluster Degradation [1] describes how to set it up and starts with this

> While the standard approach ensures service reliability and leverages Kubernetes' self-healing capabilities, there are scenarios where operating with a temporarily degraded cluster may be acceptable. This is particularly relevant for PostgreSQL clusters relying on node-local storage, where the storage is local to the Kubernetes worker node running the PostgreSQL database. Node-local storage, or simply local storage, is employed to enhance performance.

[0] https://cloudnative-pg.io/docs/devel/#main-features [1] https://cloudnative-pg.io/docs/devel/kubernetes_upgrade/#tem...