When I did my authentik setup through helm chart a while back, the only real problems I had were with learning blueprints and not so much with getting Authentik to do its thing.
The main things you should be checking given a liveliness probe failure is kubectl -n <namespace> describe pod <podname> to check the reason for failure. Additionally, kubectl logs -p -n <namespace> <podname> [container]. Will get you logs of the last run of the pod that has already failed, rather than the current run that may be soon to fail. Those two commands should point you pretty directly where your chart config has gone wrong. I can likely help as well if you are unsure what you are looking at.
Additionally, once you get things working, please go back and usw secrets properly with the chart. Authentik lets you sub many values for env vars or files, which combined with mounting secrets is how you can use them.



Coming back and checking the values file posted. Not sure why your authentik block won’t get used in your values file. Your current issue of non-starting is likely the Authentik server container starting successfully, but failing liveness while waiting for the worker container(s) that is definitely not spooling up with your current configuration.
Something to denote about Authentik itself that won’t be well-explained by the quickstart for the Helm chart itself is that Authentik is split into two containers:
serverandworker. For most environment variabless and mounted secrets, both theserverandworkerdefinitions should have them applied. The chart tends to handle most of the essential shared stuff in the authentik block to prevent the duplication, but secrets will likely need to be mounted for both volumes if using file or env references in the shared config, as well as most env overrides will need to be applied for both.