Rework metrics and logs of housekeeping tasks
A follow-up of #5584 (closed) and !6551 (merged).
The above issues are for implementing housekeeping tasks. To make them compatible with the transaction manager, they need to integrate into the life cycle of a transaction, including preparation, verification, and application. When a task spans multiple steps, metrics, stats, and logs should be revisited. We need to ensure they are still relevant and reflect the housekeeping status accurately. It's also reasonable to split them out by adding "stage" label to existing metrics.