EXPERIMENTAL: do not close binlog connection on commit error

[shlomi-noach]

Description

Looking to see if/which tests fail if we do not close the connection on commit error. I suspect nothing will fail in the tests, because this particular error is so rare. Let's see what happens and continue the investigation from there on.

Related Issue(s)

#17248

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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[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Project coverage is 67.92%. Comparing base (3499a77) to head (88b8b61).
Report is 40 commits behind head on main.

Additional details and impacted files

@@            Coverage Diff             @@
##             main   #17253      +/-   ##
==========================================
+ Coverage   67.39%   67.92%   +0.52%     
==========================================
  Files        1570     1578       +8     
  Lines      252903   261275    +8372     
==========================================
+ Hits       170451   177459    +7008     
- Misses      82452    83816    +1364     

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[shlomi-noach]

As expected, all checks pass.