This is an automated cherry-pick of #58135

What problem does this PR solve?

Issue Number: close #58031

Problem Summary:

The previous lag calculation relied on c.lastCheckpoint.TS to compute the lag. However, this approach is unreliable, especially when ownership changes, as c.lastCheckpoint.TS is not guaranteed to increase steadily. This PR addresses the issue by introducing a global checkpoint timestamp that maintains a strictly non-decreasing state.

What changed and how does it work?

The lag calculation now utilizes a global checkpoint timestamp instead of c.lastCheckpoint.TS. This global timestamp ensures consistency and stability, as it always increases or stays the same, even during ownership transitions. This change guarantees a more robust and accurate lag measurement.

Check List

Tests

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

  • I checked and no code files have been changed.

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

Please refer to Release Notes Language Style Guide to write a quality release note.

Fix this issue that when new advancer owner starts the task unexpected paused due to last checkpoint ts equal to start ts