sink: add async ddl timeout for add index (#5836)

[ti-chi-bot]

This is an automated cherry-pick of #5836

What problem does this PR solve?

Issue Number: close #5711 close #1926

What is changed and how it works?

The change adds a dedicated timeout path for TiDB async DDL, specifically ADD INDEX.
Added a new MySQL sink option async-ddl-timeout, the default value is 10s. It can be set in sink URI: mysql://.../?async-ddl-timeout=30m

• The sink now uses separate DB pools:
  • dmlDB: DML writes.
  • controlDB: normal DDL, DDL-ts, syncpoint, progress metadata, etc.
  • controlAsyncDB: only for TiDB ADD INDEX. controlAsyncDB is created only when the downstream is confirmed to be TiDB.
• DDL execution now chooses the DB based on DDL type:
  • TiDB ADD INDEX uses controlAsyncDB and async-ddl-timeout.
  • All other DDLs use controlDB and the normal read-timeout.

Check List

Tests

• Unit test
• Integration test

Questions

Will it cause performance regression or break compatibility?

Do you need to update user documentation, design documentation or monitoring documentation?

Release note

Please refer to [Release Notes Language Style Guide](https://pingcap.github.io/tidb-dev-guide/contribute-to-tidb/release-notes-style-guide.html) to write a quality release note.

If you don't think this PR needs a release note then fill it with `None`.

Summary by CodeRabbit

• New Features

  • Added configurable asynchronous DDL timeouts for TiDB downstreams.
  • TiDB ADD INDEX operations now use a dedicated asynchronous connection with its own timeout.
  • Async DDL timeout settings are supported through sink configuration, API, and configuration files.

• Bug Fixes

  • Improved timeout handling while preserving existing settings for other DDL operations.
  • MySQL operations continue using the standard control connection.
  • Invalid asynchronous DDL timeout values are rejected with validation errors.

[ti-chi-bot]

This cherry pick PR is for a release branch and has not yet been approved by triage owners.
Adding the do-not-merge/cherry-pick-not-approved label.

To merge this cherry pick:

1. It must be LGTMed and approved by the reviewers firstly.
2. For pull requests to TiDB-x branches, it must have no failed tests.
3. AFTER it has lgtm and approved labels, please wait for the cherry-pick merging approval from triage owners.

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[ti-chi-bot]

@wk989898 This PR has conflicts, I have hold it.
Please resolve them or ask others to resolve them, then comment /unhold to remove the hold label.

[ti-chi-bot]

@ti-chi-bot: ## If you want to know how to resolve it, please read the guide in TiDB Dev Guide.

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[APPROVALNOTIFIER] This PR is NOT APPROVED

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