[release-20.0] VTAdmin: Fix serve-handler's path-to-regexp dep and add default schema refresh (#16778)

[vitess-bot]

Description

This is a backport of #16778

[vitess-bot]

Review Checklist

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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.

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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 68.65%. Comparing base (4a0aab6) to head (138a7d5).
Report is 1 commits behind head on release-20.0.

Additional details and impacted files

@@               Coverage Diff                @@
##           release-20.0   #16784      +/-   ##
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- Coverage         68.68%   68.65%   -0.03%     
================================================
  Files              1541     1541              
  Lines            197937   197937              
================================================
- Hits             135945   135893      -52     
- Misses            61992    62044      +52     

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