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

[thotaDeepika]

• Fix binary search with duplicates issue Binary Search gives wrong output for duplicate elements TheAlgorithms/Python#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

• 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

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Describe your change:

• Add an algorithm?
• Fix a bug or typo in an existing algorithm?
• Add or change doctests? -- Note: Please avoid changing both code and tests in a single pull request.
• Documentation change?

Checklist:

• I have read CONTRIBUTING.md.
• This pull request is all my own work -- I have not plagiarized.
• I know that pull requests will not be merged if they fail the automated tests.
• This PR only changes one algorithm file. To ease review, please open separate PRs for separate algorithms.
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