tici: add some log and metrics for debug

[wshwsh12]

What problem does this PR solve?

Issue Number: close #xxx

Problem Summary:

What is changed and how it works?

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

None

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[ChangRui-Ryan]

lgtm

[wshwsh12]

/retest

[JaySon-Huang]

Better use start_ts that is widely used in other places for logging in TiFlash.

[ti-chi-bot]

[APPROVALNOTIFIER] This PR is APPROVED

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

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• OWNERS [JaySon-Huang,JinheLin]

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[ti-chi-bot]

[LGTM Timeline notifier]

Timeline:

• 2026-02-10 09:26:01.426070061 +0000 UTC m=+263377.120209901: ☑️ agreed by JinheLin.
• 2026-02-13 10:40:07.923847329 +0000 UTC m=+5775.670241362: ☑️ agreed by JaySon-Huang.