Currently, CockroachDB has subsystems (e.g. SQL Stats) that holds data in-memory and flushes them into system tables periodically.
When a node shuts down, these subsystems should be notified and start to flush their in-memory data into system tables, otherwise the in-memory data will just simply be deleted and cannot be recovered.
This becomes an issue in Serverless clusters, where the tenant node is shutdown after a period of inactivity, (usually less than the flush interval).

CRDB's current shutdown process looks like following:

shutdown requested -> block incoming sql traffic -> start draining -> stop stopper

We would like to introduce additional stage in the shutdown process:

shutdown requested -> block incoming sql traffic -> run final sql -> start draining -> stop stopper

This allows subsystems like SQL Stats to have a chance to flush its in-memory data during the graceful shutdown.

cc: @cockroachdb/server
cc: @cockroachdb/sql-observability

Epic CRDB-11087