Playbook unable to write to persistent volume

Container Group is not kubernetes-thing, but AWX-thing.

My guide also provides some guide to use Container Group, I think this guide is a bit excessive for your requirements: https://github.com/kurokobo/awx-on-k3s/tree/main/containergroup

For your use case:

Create new Container Group by Administration > Instance Group > Add > Add container group, and enable Customize pod specification, then define specification as following:

apiVersion: v1
kind: Pod
metadata:
  namespace: awx
spec:
  serviceAccountName: default
  automountServiceAccountToken: false
  containers:
    - image: quay.io/ansible/awx-ee:latest
      name: worker
      args:
        - ansible-runner
        - worker
        - '--private-data-dir=/runner'
      resources:
        requests:
          cpu: 250m
          memory: 100Mi
      volumeMounts:
        - name: demo-volume
          mountPath: /data/esxi-config-backups
  volumes:
    - name: demo-volume
      persistentVolumeClaim:
        claimName: esxi-config-backups-claim

Then specify this Container Group as Instance Groups in the Job Template.