go.mod: upgrade tiflow to support partial index and add related tests (#3699)

[YangKeao]

What problem does this PR solve?

Issue Number: close #3698

What is changed and how it works?

Upgrade the TiCDC to support partial index.

Check List

Tests

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

It's manually tested with https://github.com/PingCAP-QE/endless/pull/3072.

Questions

Will it cause performance regression or break compatibility?

This is a manual cherry pick of #3699

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

Release note

None

Summary by CodeRabbit

• Chores

  • Updated dependencies: go-mysql to v1.13.0, tidb/tiflow to a newer revision, and adjusted gRPC to v1.65.0.

• Tests

  • Added integration tests covering partial index creation and data scenarios.
  • Added test runner and configuration to validate partial-index behavior.
  • Expanded CI test matrix to include partial_index across all sink types.

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[YangKeao]

Ref pingcap/tiflow#12686, not finished yet.
/hold

[ti-chi-bot]

[APPROVALNOTIFIER] This PR is APPROVED

This pull-request has been approved by: hongyunyan, wk989898

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• OWNERS [hongyunyan,wk989898]

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[ti-chi-bot]

[LGTM Timeline notifier]

Timeline:

• 2026-06-11 01:08:36.694093195 +0000 UTC m=+1008617.764410585: ☑️ agreed by hongyunyan.
• 2026-06-11 01:26:53.529656769 +0000 UTC m=+1009714.599974159: ☑️ agreed by wk989898.