pool: reopen connection closed by idle timeout

[harshit-gangal]

Description

This PR complements the earlier change made in #17757 by further refining the connection pool’s idle timeout behavior.

This implementation reduces connection churn. Instead of simply closing idle connections, they will now be closed and immediately reopened. This ensures that connections remain fresh and available, preventing unnecessary delays caused by frequent connection creation during traffic spikes.

Backport Reason: The previous iteration of this change was backported, so this update should be backported as well to maintain consistency and ensure the improvements apply across all relevant versions.

Related Issue(s)

• Closes Reduce Connection Churn and p99 Spikes by Idle Connections Timeout #17819

Checklist

• "Backport to:" labels have been added if this change should be back-ported to release branches
• If this change is to be back-ported to previous releases, a justification is included in the PR description
• Tests were added or are not required
• Did the new or modified tests pass consistently locally and on CI?
• Documentation was added or is not required

Deployment Notes

[vitess-bot]

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[vitess-bot]

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[codecov]

Codecov Report

Attention: Patch coverage is 70.58824% with 5 lines in your changes missing coverage. Please review.

Project coverage is 67.46%. Comparing base (67d081a) to head (fc9a7e2).
Report is 5 commits behind head on main.

Files with missing lines	Patch %	Lines
go/pools/smartconnpool/pool.go	70.58%	5 Missing ⚠️

Additional details and impacted files

@@            Coverage Diff             @@
##             main   #17818      +/-   ##
==========================================
+ Coverage   67.41%   67.46%   +0.04%     
==========================================
  Files        1592     1592              
  Lines      258024   258157     +133     
==========================================
+ Hits       173948   174156     +208     
+ Misses      84076    84001      -75     

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[vmg]

Looks great. Appreciate the new tests!