Fix binary search to return leftmost occurrence for duplicates

[CommitToday]

Overview
This PR fixes issue #13887 by modifying the binary search implementation to return the index of the leftmost occurrence when there are multiple occurrences of the search item in the sorted collection. Previously, the function would return any arbitrary occurrence.

Checklist

• Code changes implemented in both iterative and recursive binary search functions
• Added test cases to verify the new behavior
• Updated docstrings to reflect the new behavior

Proof
The changes include:

1. Modified the iterative binary_search function to continue searching to the left after finding a match to locate the leftmost occurrence
2. Rewrote the recursive binary_search_by_recursion function with an inner helper function that properly handles finding the leftmost occurrence
3. Added specific test cases like binary_search([1, 2, 4, 4, 4, 6, 7], 4) which should return 2 (the index of the leftmost occurrence of 4)
4. Updated docstrings to clearly document that the function returns the leftmost occurrence when duplicates exist

Fixes #13841
Fixes #13887
Fixes #13901
Fixes #13955
Fixes #14051
Fixes #14456
Fixes #14622
Fixes #14708