*: report unhealthy on the status port when the memory usage is too high

[djshow832]

What problem does this PR solve?

Issue Number: close #1119

Problem Summary:
#1120 only rejects connections when the memory is too high, but it doesn't report unhealthy on the status port.

What is changed and how it works:

• Add a health manager, which manages the health status
• The health manager queries the server and memory manager to get the status
• The API server and proxy server reads the health manager

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

[codecov-commenter]

Codecov Report

❌ Patch coverage is 76.05634% with 17 lines in your changes missing coverage. Please review.
⚠️ Please upload report for BASE (main@9031e2d). Learn more about missing BASE report.

Files with missing lines	Patch %	Lines
cmd/replayer/main.go	0.00%	10 Missing ⚠️
pkg/server/server.go	56.25%	6 Missing and 1 partial ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##             main    #1212   +/-   ##
=======================================
  Coverage        ?   67.71%           
=======================================
  Files           ?      152           
  Lines           ?    16915           
  Branches        ?        0           
=======================================
  Hits            ?    11454           
  Misses          ?     4692           
  Partials        ?      769           

Flag	Coverage Δ
unit	67.71% <76.05%> (?)

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[djshow832]

/retest

[YangKeao]

LGTM

[ti-chi-bot]

[APPROVALNOTIFIER] This PR is APPROVED

This pull-request has been approved by: YangKeao

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Needs approval from an approver in each of these files:

• OWNERS [YangKeao]

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[ti-chi-bot]

[LGTM Timeline notifier]

Timeline:

• 2026-09-10 16:22:21.979207278 +0000 UTC m=+1987577.150301394: ☑️ agreed by YangKeao.

[djshow832]

/cherry-pick release-1.3

[ti-chi-bot]

@djshow832: The label(s) /release-1.3 cannot be applied, because the repository doesn't have them.

Details

In response to this:

/cherry-pick release-1.3

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[ti-chi-bot]

@djshow832: new pull request created to branch release-1.3: #1214.
But this PR has conflicts, please resolve them!

Details

In response to this:

/cherry-pick release-1.3

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[djshow832]

/cherry-pick release-nextgen-202603

[ti-chi-bot]

@djshow832: The label(s) /release-nextgen-202603 cannot be applied, because the repository doesn't have them.

Details

In response to this:

/cherry-pick release-nextgen-202603

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[ti-chi-bot]

@djshow832: new pull request created to branch release-nextgen-202603: #1215.

Details

In response to this:

/cherry-pick release-nextgen-202603

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 ti-community-infra/tichi repository.