Support graceful shutdown in TiFlash (release-8.5)

[gengliqi]

What problem does this PR solve?

Issue Number: close #10266

Problem Summary:
Cherry-pick #10299 and #10313 and #10317 to release-8.5

What is changed and how it works?

Support graceful shutdown in TiFlash

Check List

Tests

• Unit test
• Integration test
• Manual test (add detailed scripts or steps below)
• No code

Side effects

• Performance regression: Consumes more CPU
• Performance regression: Consumes more Memory
• Breaking backward compatibility

Documentation

• Affects user behaviors
• Contains syntax changes
• Contains variable changes
• Contains experimental features
• Changes MySQL compatibility

Release note

Support graceful shutdown in TiFlash

[windtalker]

lgtm

[ti-chi-bot]

[APPROVALNOTIFIER] This PR is APPROVED

This pull-request has been approved by: JaySon-Huang, windtalker

The full list of commands accepted by this bot can be found here.

The pull request process is described here

Details

Needs approval from an approver in each of these files:

• OWNERS [JaySon-Huang,windtalker]

Approvers can indicate their approval by writing /approve in a comment
Approvers can cancel approval by writing /approve cancel in a comment

[ti-chi-bot]

[LGTM Timeline notifier]

Timeline:

• 2025-08-28 14:03:57.488209765 +0000 UTC m=+448929.366040719: ☑️ agreed by JaySon-Huang.
• 2025-09-01 02:38:55.196777169 +0000 UTC m=+753427.074608123: ☑️ agreed by windtalker.