[release-19.0] prevent vtctld from creating tons of S3 connections (#15296)

[vitess-bot]

Description

This is a backport of #15296

[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.

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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

Attention: Patch coverage is 85.71429% with 1 lines in your changes are missing coverage. Please review.

Project coverage is 67.44%. Comparing base (977b585) to head (2c59593).
Report is 1 commits behind head on release-19.0.

Files	Patch %	Lines
go/vt/mysqlctl/s3backupstorage/s3.go	85.71%	1 Missing ⚠️

Additional details and impacted files

@@               Coverage Diff                @@
##           release-19.0   #15401      +/-   ##
================================================
+ Coverage         67.43%   67.44%   +0.01%     
================================================
  Files              1560     1560              
  Lines            192581   192632      +51     
================================================
+ Hits             129858   129924      +66     
+ Misses            62723    62708      -15     

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