PYTHON-6022 Consolidate all non-IO code in AsyncCursor/Cursor into _A…

[NoahStapp]

…gnosticCursor

PYTHON-6022

Changes in this PR

See ticket.

Test Plan

Existing tests.

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

❌ Patch coverage is 92.88026% with 22 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
pymongo/cursor_shared.py	92.64%	14 Missing and 8 partials ⚠️

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