Fix flakiness in TestListenerShutdown

[frouioui]

Description

This is a follow up of #16940 where the test was modified to alleviate flakiness.

This PR aims at removing (or at least reducing) the flakiness observed on TestListenerShutdown. This test almost never fails on this repository's CI, but I have observed several failures in other repositories where the CI is less beefy. The original error was:

--- FAIL: TestListenerShutdown (10.00s)
    server_test.go:265: listening on address '127.0.0.1' port 41183
    server_test.go:1448: 
        	Error Trace:	/opt/actions-runner/_work/vitess-private/vitess-private/go/mysql/server_test.go:1448
        	            				/opt/actions-runner/_work/vitess-private/vitess-private/go/mysql/server_test.go:1427
        	Error:      	connRefuse did not reach %v
        	Test:       	TestListenerShutdown
        	Messages:   	1
FAIL
FAIL	vitess.io/vitess/go/mysql	39.529s

I ran this fix ten times in another repository where the issue was first observed, and it passed successfully the ten times.

[vitess-bot]

Review Checklist

Hello reviewers! 👋 Please follow this checklist when reviewing this Pull Request.

General

• Ensure that the Pull Request has a descriptive title.
• Ensure there is a link to an issue (except for internal cleanup and flaky test fixes), new features should have an RFC that documents use cases and test cases.

Tests

• Bug fixes should have at least one unit or end-to-end test, enhancement and new features should have a sufficient number of tests.

Documentation

• Apply the release notes (needs details) label if users need to know about this change.
• New features should be documented.
• There should be some code comments as to why things are implemented the way they are.
• There should be a comment at the top of each new or modified test to explain what the test does.

New flags

• Is this flag really necessary?
• Flag names must be clear and intuitive, use dashes (-), and have a clear help text.

If a workflow is added or modified:

• Each item in Jobs should be named in order to mark it as required.
• If the workflow needs to be marked as required, the maintainer team must be notified.

Backward compatibility

• Protobuf changes should be wire-compatible.
• Changes to _vt tables and RPCs need to be backward compatible.
• RPC changes should be compatible with vitess-operator
• If a flag is removed, then it should also be removed from vitess-operator and arewefastyet, if used there.
• vtctl command output order should be stable and awk-able.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 67.16%. Comparing base (9c9a893) to head (e19acbc).
Report is 24 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main   #17024      +/-   ##
==========================================
- Coverage   67.17%   67.16%   -0.01%     
==========================================
  Files        1571     1571              
  Lines      252249   252249              
==========================================
- Hits       169459   169434      -25     
- Misses      82790    82815      +25     

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

[mattlord]

Thanks!

[deepthi]

❤️