[release-23.0] Change connection pool idle expiration logic (#19004)

[vitess-bot]

Description

This is a backport of #19004

[vitess-bot]

Review Checklist

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General

• Ensure that the Pull Request has a descriptive title.
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Backward compatibility

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[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 69.71%. Comparing base (30a3d9c) to head (e6d3626).
⚠️ Report is 1 commits behind head on release-23.0.

Additional details and impacted files

@@               Coverage Diff                @@
##           release-23.0   #19014      +/-   ##
================================================
- Coverage         69.71%   69.71%   -0.01%     
================================================
  Files              1606     1606              
  Lines            214570   214584      +14     
================================================
+ Hits             149589   149591       +2     
- Misses            64981    64993      +12     

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