chore(go): bump Go version to 1.25.6 across modules (#10211)

[ti-chi-bot]

This is an automated cherry-pick of #10211

What problem does this PR solve?

Issue Number: Close #10210.

What is changed and how does it work?

Update `go.mod` files for the main project, client, tools, and integration tests to target Go `1.25.6` for consistent builds and tooling.

Check List

Tests

• Unit test
• Integration test

Release note

None.

Summary by CodeRabbit

• Chores
  • Upgraded Go toolchain to version 1.25.6 across build environments.

[ti-chi-bot]

This cherry pick PR is for a release branch and has not yet been approved by triage owners.
Adding the do-not-merge/cherry-pick-not-approved label.

To merge this cherry pick:

1. It must be LGTMed and approved by the reviewers firstly.
2. For pull requests to TiDB-x branches, it must have no failed tests.
3. AFTER it has lgtm and approved labels, please wait for the cherry-pick merging approval from triage owners.

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[ti-chi-bot]

@JmPotato 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]

@ti-chi-bot: ## If you want to know how to resolve it, please read the guide in TiDB Dev Guide.

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[ti-chi-bot]

[APPROVALNOTIFIER] This PR is NOT APPROVED

This pull-request has been approved by:
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[ti-chi-bot]

@ti-chi-bot: The following tests failed, say /retest to rerun all failed tests or /retest-required to rerun all mandatory failed tests:

Test name	Commit	Details	Required	Rerun command
pull-unit-test-next-gen-2	93f6855	link	true	/test pull-unit-test-next-gen-2
pull-unit-test-next-gen-3	93f6855	link	true	/test pull-unit-test-next-gen-3
pull-unit-test-next-gen-1	93f6855	link	true	/test pull-unit-test-next-gen-1

Full PR test history. Your PR dashboard.

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[codecov]

Codecov Report

❌ Patch coverage is 86.00000% with 7 lines in your changes missing coverage. Please review.
✅ Project coverage is 78.64%. Comparing base (14fe15c) to head (93f6855).
⚠️ Report is 2 commits behind head on release-nextgen-20251011.

Additional details and impacted files

@@                     Coverage Diff                      @@
##           release-nextgen-20251011   #10222      +/-   ##
============================================================
- Coverage                     78.73%   78.64%   -0.09%     
============================================================
  Files                           491      491              
  Lines                         66124    66320     +196     
============================================================
+ Hits                          52060    52155      +95     
- Misses                        10308    10397      +89     
- Partials                       3756     3768      +12     

Flag	Coverage Δ
unittests	78.64% <86.00%> (-0.09%)	⬇️

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