Make /api/debug/health return error when no backends are available

[djshow832]

What problem does this PR solve?

Issue Number: close #689

Problem Summary:
When TiProxy starts, it may take some time to connect to PD and update the backend status. During this phase, no connections should be routed to this instance. So the HTTP API /api/debug/health should report an error when there's no available backends.

What is changed and how it works:

• Add an interface NamespaceManager and test /api/debug/health with a mocked one.
• NamespaceManager.Ready() returns true only when all the routers have at least one healthy backend.
• /api/debug/health returns OK only when NamespaceManager.Ready() and the server is not closing.

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.

- Make /api/debug/health return error when no backends are available

[djshow832]

/retest

[codecov-commenter]

Codecov Report

Attention: Patch coverage is 67.56757% with 12 lines in your changes missing coverage. Please review.

Please upload report for BASE (main@4243fb5). Learn more about missing BASE report.

Files with missing lines	Patch %	Lines
pkg/manager/namespace/manager.go	71.42%	6 Missing ⚠️
pkg/balance/router/router_score.go	75.00%	2 Missing and 1 partial ⚠️
pkg/balance/router/router_static.go	0.00%	2 Missing ⚠️
pkg/proxy/backend/handshake_handler.go	0.00%	1 Missing ⚠️

Additional details and impacted files

@@           Coverage Diff           @@
##             main     #692   +/-   ##
=======================================
  Coverage        ?   69.88%           
=======================================
  Files           ?      105           
  Lines           ?    10015           
  Branches        ?        0           
=======================================
  Hits            ?     6999           
  Misses          ?     2523           
  Partials        ?      493           

Flag	Coverage Δ
unit	69.88% <67.56%> (?)

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[ti-chi-bot]

[APPROVALNOTIFIER] This PR is APPROVED

This pull-request has been approved by: xhebox

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• OWNERS [xhebox]

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[ti-chi-bot]

[LGTM Timeline notifier]

Timeline:

• 2024-09-27 08:06:50.06774843 +0000 UTC m=+1812479.808172369: ☑️ agreed by xhebox.