[Searches] Fix Binary Search bug with duplicate elements (#13946)

* Fix binary search with duplicates issue #13886

* Add docstrings to binary search functions

Added docstrings for lower_bound and upper_bound functions.

* [pre-commit.ci] auto fixes from pre-commit.com hooks

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* Update searches/binary_search.py

Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>

* Refactor docstrings for lower_bound and upper_bound

Updated docstring parameter and return type annotations for lower_bound and upper_bound functions.

* Update searches/binary_search.py

Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>

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Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
Co-authored-by: Copilot <175728472+Copilot@users.noreply.github.com>
Co-authored-by: John Law <johnlaw.po@gmail.com>