Pods are considered ready while loading and cannot serve

Related: https://github.com/dragonflydb/dragonfly/issues/5881

Problem:
Currently, using the standard Docker healthcheck for both liveness and readiness probes causes issues during rolling updates when:
- New pods pass health checks while still loading datasets into memory
- Kubernetes kills old pods before new pods are truly ready to serve traffic
- This results in service downtime during deployments (3+ minutes as mentioned in #5881)

Start with the related issue #5881 and trace how the standard Docker healthcheck is used for liveness and readiness in the operator's pod configuration. Done means new pods are not marked ready until dataset loading completes and rolling updates avoid routing traffic early or killing old pods; the issue names no files or tests.

Written by the indexing model from the issue text.