PYTHON-6122 Address flakiness in command logging, retryable reads, and retryable writes unified tests for retryable handshake errors

[NoahStapp]

PYTHON-6122

Changes in this PR

See ticket.

Test Plan

Unified test changes.

Checklist

Checklist for Author

• Did you update the changelog (if necessary)?
• Is there test coverage?
• Is any followup work tracked in a JIRA ticket? If so, add link(s).

Checklist for Reviewer

• Does the title of the PR reference a JIRA Ticket?
• Do you fully understand the implementation? (Would you be comfortable explaining how this code works to someone else?)
• Is all relevant documentation (README or docstring) updated?

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.

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