Check when a new version is released here and check if it has been updated here, usually they only change the version of the operator image in that file.
Usually we should keep them in sync, the vitess-operator image and the vitess image.
When upgrading make sure you specify here the latest version used, so it will be easier to see what version we are using:
kubectl apply -f https://raw.githubusercontent.com/vitessio/vitess/v14.0.0/examples/operator/operator.yaml
# Vitess operator 2.7.1
kubectl get pod
# Logs
kubectl logs -f vitess-operator-647f7cc94f-zgf9q
Sometimes you might need to restart the backends, because this might trigger a restart for the vitess, and the backend sometimes doesn't refresh the connection ot the db. Check the logs of the backend.