*: upgrade go to 1.25.10

[djshow832]

What problem does this PR solve?

Issue Number: close #xxx

Problem Summary:
Upgrade go because of EE requirement.

What is changed and how it works:
Upgrade go and fix lint.
verifyPeerCertificates is updated because VerifyConnection also verifies resumed sessions, and ConnectionState.PeerCertificates is already parsed and can be reused.

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.

None

[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.

Details

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[codecov-commenter]

Codecov Report

❌ Patch coverage is 76.92308% with 9 lines in your changes missing coverage. Please review.
⚠️ Please upload report for BASE (release-1.3@6b80686). Learn more about missing BASE report.

Files with missing lines	Patch %	Lines
lib/cli/util.go	0.00%	3 Missing ⚠️
pkg/proxy/net/packetio.go	33.33%	0 Missing and 2 partials ⚠️
lib/config/proxy.go	0.00%	1 Missing ⚠️
pkg/balance/router/router.go	0.00%	1 Missing ⚠️
pkg/proxy/net/proxy.go	50.00%	0 Missing and 1 partial ⚠️
pkg/util/lex/lex.go	83.33%	1 Missing ⚠️

Additional details and impacted files

@@              Coverage Diff               @@
##             release-1.3    #1113   +/-   ##
==============================================
  Coverage               ?   65.55%           
==============================================
  Files                  ?      125           
  Lines                  ?    12313           
  Branches               ?        0           
==============================================
  Hits                   ?     8072           
  Misses                 ?     3700           
  Partials               ?      541           

Flag	Coverage Δ
unit	65.55% <76.92%> (?)

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[YangKeao]

LGTM

[ti-chi-bot]

[APPROVALNOTIFIER] This PR is APPROVED

This pull-request has been approved by: YangKeao

The full list of commands accepted by this bot can be found here.

The pull request process is described here

Details

Needs approval from an approver in each of these files:

• OWNERS [YangKeao]

Approvers can indicate their approval by writing /approve in a comment
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[ti-chi-bot]

[LGTM Timeline notifier]

Timeline:

• 2026-06-01 09:18:18.444507775 +0000 UTC m=+173999.514825155: ☑️ agreed by YangKeao.

[djshow832]

LGTM

[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.

Details

Instructions for interacting with me using PR comments are available here. If you have questions or suggestions related to my behavior, please file an issue against the kubernetes-sigs/prow repository.