release-25.4: persistedsqlstats: add WithCancelOnQuiesce to MaybeFlushWithDrainer

[kyle-a-wong]

Backport 1/1 commits from #160403.

/cc @cockroachdb/release

---

use context from stopper.WithCancelOnQuiesce(ctx) to prevent slow slow quiesce during shutdown

Epic: None
Fixes: #159467
Release note: None

Release Justification: Low risk change that prevents slow quiesce during shutdowns. This has been seen in 25.4 (#161060), so we are backporting.

[blathers-crl]

Thanks for opening a backport.

Before merging, please confirm that it falls into one of the following categories (select one):

• Non-production code changes. Includes test-only changes, build system changes, etc.
• Fixes for serious issues. Defined in the policy as correctness, stability, or security issues, data corruption/loss, significant performance regressions, breaking working and widely used functionality, or an inability to detect and debug production issues.
• Other approved changes. These changes must be gated behind a disabled-by-default feature flag unless there is a strong justification not to.

Add a brief release justification to the PR description explaining your selection.

Also, confirm that the change does not break backward compatibility and complies with all aspects of the backport policy.

All backports must be reviewed by the TL and EM for the owning area.

[blathers-crl]

It looks like your PR touches production code but doesn't add or edit any test code. Did you consider adding tests to your PR?

_{🦉 Hoot! I am a Blathers, a bot for CockroachDB. My owner is dev-inf.}

[cockroach-teamcity]

This change is 

[blathers-crl]

✅ PR #161177 is compliant with backport policy

Confidence: high
Critical bug criteria met: [Stability or security issues]
Backward compatible: true
Explanation: The pull request has a valid release justification which states it is a 'Low risk change that prevents slow quiesce during shutdowns.' This change can be classified as addressing a stability issue which is part of the critical bug criteria. The fix deals with shutdown operations, potentially resolving a stability problem during shutdown sequences, which justifies it as a critical bug fix. Furthermore, the PR does not introduce or remove feature flags nor does it show indications of breaking backward compatibility as the change is localized to handling shutdown sequences efficiently. Given these conditions, there is no need to assess feature flag inclusion separately in this case.

_{🦉 Hoot! I am a Blathers, a bot for CockroachDB. My owner is dev-inf.}