Adding Database to raspberry pi kubernetes cluster

Easiest thing is to set up NFS server on master node, export your USB drive over NFS and then mount it as Persistent Volume in pod. For this you need first to create PersistentVolume:

apiVersion: v1kind: PersistentVolumemetadata:  name: nfsspec:  capacity:    storage: 5Gi  accessModes:    - ReadWriteMany  nfs:    server: master-node-ip    path: /mnt/nfsserver

And then create PersistentVolumeClaim of the same size:

apiVersion: v1kind: PersistentVolumeClaimmetadata:  name: nfsspec:  accessModes:    - ReadWriteMany  storageClassName: ""  resources:    requests:      storage: 5Gi

After that you can mount this PVC on all needed pods:

    volumeMounts:    - name: nfs      mountPath: "/usr/share/nginx/html"  volumes:  - name: nfs    persistentVolumeClaim:      claimName: nfs

If I mount a local volume to the master node, will I be able to run a postgres container in a worker node and access the volume mounted on the master node?

No. You will need to run something to make your volume accessible to other nodes. There are tons of filesystems for that purpose (Ceph, Lustre, even NFS, etc.) And there are starting to be Kubernetes native ones too (i.e. Rook.)