metrics: add circuit breaker metrics (#59338)

[ti-chi-bot]

This is an automated cherry-pick of #59338

What problem does this PR solve?

Issue Number: ref #58780

Problem Summary:

What changed and how does it work?

Check List

Tests

• [x] Manual test (add detailed scripts or steps below)

Release note

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

None

[ti-chi-bot]

@rleungx 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[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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[EmmaDuDu]

/retest

[rleungx]

/hold cancel

[codecov[bot]]

Codecov Report

:white_check_mark: All modified and coverable lines are covered by tests. :warning: Please upload report for BASE (release-8.5@616e914). Learn more about missing BASE report.

Additional details and impacted files

@@               Coverage Diff                @@
##             release-8.5     #64972   +/-   ##
================================================
  Coverage               ?   77.1037%           
================================================
  Files                  ?       1683           
  Lines                  ?     467562           
  Branches               ?          0           
================================================
  Hits                   ?     360508           
  Misses                 ?      84873           
  Partials               ?      22181           

Flag	Coverage Δ
integration	50.7427% <ø> (?)
unit	72.1755% <ø> (?)

Flags with carried forward coverage won't be shown. Click here to find out more.

Components	Coverage Δ
dumpling	52.9278% <0.0000%> (?)
parser	∅ <0.0000%> (?)
br	64.7303% <0.0000%> (?)

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[ti-chi-bot[bot]]

[APPROVALNOTIFIER] This PR is APPROVED

This pull-request has been approved by: lcwangchao, okJiang

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Needs approval from an approver in each of these files:

• ~~OWNERS~~ [lcwangchao,okJiang]

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[bot]]

[LGTM Timeline notifier]

Timeline:

• 2025-12-15 04:55:52.096422779 +0000 UTC m=+1448896.910200350: :ballot_box_with_check: agreed by lcwangchao.
• 2025-12-15 05:41:06.570087791 +0000 UTC m=+1451611.383865363: :ballot_box_with_check: agreed by okJiang.