Add logging to binlog watcher actions

[BenjaminLockhart]

Description

Adding visibility to certain binlog watcher and VStream actions so that they can be more accurately triaged after an outage.

Related Issue(s)

Fixes: #18255

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]

Review Checklist

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

General

• Ensure that the Pull Request has a descriptive title.
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Tests

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• 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 67.49%. Comparing base (2520f7f) to head (8cfa316).
Report is 40 commits behind head on main.

Additional details and impacted files

@@           Coverage Diff           @@
##             main   #18264   +/-   ##
=======================================
  Coverage   67.49%   67.49%           
=======================================
  Files        1603     1603           
  Lines      262428   262429    +1     
=======================================
+ Hits       177114   177137   +23     
+ Misses      85314    85292   -22     

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[harshit-gangal]

you need to sign the commit. DCO is complaining.

[github-actions]

This PR is being marked as stale because it has been open for 30 days with no activity. To rectify, you may do any of the following:

• Push additional commits to the associated branch.
• Remove the stale label.
• Add a comment indicating why it is not stale.

If no action is taken within 7 days, this PR will be closed.