Fix incorrect output in Binary Search when duplicates exist(Fixes #13840)

[tusharynayaka]

Description of Change
Updated the binary search algorithm to return the first occurrence of an item when duplicates exist in the collection, rather than returning any random occurrence.
Added a check to see if the element immediately to the left of the found midpoint is also the target item.
If it is, the search continues to the left side to find the true first index.
Updated doctests to verify this behavior.

Checklist:
[x] I have read CONTRIBUTING.md.
[x] This pull request is all my own work -- I have not plagiarized.
[x] I know that pull requests will not be merged if they fail the automated tests.
[x] This PR only changes one algorithm file.
[x] All filenames are in all lowercase characters with no spaces or dashes.
[x] All functions and variable names follow Python naming conventions.
[x] All function parameters and return values are annotated with Python type hints.
[x] All functions have doctests that pass the automated testing.
[x] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a closing keyword: Fixes #13840

[algorithms-keeper]

Closing this pull request as invalid

@tusharynayaka, this pull request is being closed as the files submitted contains an invalid extension. This repository only accepts Python algorithms. Please read the Contributing guidelines first.

Invalid files in this pull request: uv.lock