proxy: reject connection after graceful wait (#525)

[djshow832]

This is a cherry-pick of #525

What problem does this PR solve?

Issue Number: close #524

Problem Summary:
In #400, I intended to accept connection during graceful wait so that client connections won't fail during tiproxy shutting down.
However, in #443, I somehow broke that behavior when I was fixing a data race.

What is changed and how it works:

• Do not reject connections during graceful-wait-before-shutdown
• Defer unlocking just in case it panics and all other connections block

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.

- Do not reject new connections until `graceful-wait-before-shutdown` finishes

[djshow832]

/retest

[codecov-commenter]

Codecov Report

Attention: Patch coverage is 81.48148% with 5 lines in your changes are missing coverage. Please review.

❗ No coverage uploaded for pull request base (serverless@d58674c). Click here to learn what that means.

Files	Patch %	Lines
pkg/proxy/proxy.go	81.48%	3 Missing and 2 partials ⚠️

Additional details and impacted files

@@              Coverage Diff              @@
##             serverless     #526   +/-   ##
=============================================
  Coverage              ?   64.37%           
=============================================
  Files                 ?       61           
  Lines                 ?     5805           
  Branches              ?        0           
=============================================
  Hits                  ?     3737           
  Misses                ?     1780           
  Partials              ?      288           

Flag	Coverage Δ
unit	64.37% <81.48%> (?)

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[ti-chi-bot]

[APPROVALNOTIFIER] This PR is APPROVED

This pull-request has been approved by: xhebox

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[ti-chi-bot]

[LGTM Timeline notifier]

Timeline:

• 2024-05-07 06:47:56.204984078 +0000 UTC m=+944629.962119650: ☑️ agreed by xhebox.