balance: fix potential data race when setting config by adding a lock (#808)

[ti-chi-bot]

This is an automated cherry-pick of #808

What problem does this PR solve?

Issue Number: close #806

Problem Summary:
When routing and setting config concurrently, the FactorBasedBalance.factors is read and written concurrently, leading a data race.

What is changed and how it works:
Add a lock in the FactorBasedBalance.

Check List

Tests

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

Notable changes

• Has configuration change
• Has HTTP API interfaces change
• Has tiproxyctl change
• Other user behavior changes

Release note

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

- Fix data race when routing and setting config concurrently.

[codecov-commenter]

Codecov Report

All modified and coverable lines are covered by tests ✅

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Additional details and impacted files

@@              Coverage Diff               @@
##             release-1.3     #809   +/-   ##
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  Coverage               ?   66.53%           
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  Files                  ?      122           
  Lines                  ?    11336           
  Branches               ?        0           
==============================================
  Hits                   ?     7542           
  Misses                 ?     3260           
  Partials               ?      534           

Flag	Coverage Δ
unit	66.53% <100.00%> (?)

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[ti-chi-bot]

[APPROVALNOTIFIER] This PR is APPROVED

This pull-request has been approved by: djshow832

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• OWNERS [djshow832]

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[ti-chi-bot]

[LGTM Timeline notifier]

Timeline:

• 2025-06-03 07:44:19.594998997 +0000 UTC m=+341345.797344261: ☑️ agreed by djshow832.