Fix Bugs and Improve Traversal Methods in Binary Search Tree Implementation

[shubhamvk03]

Describe your change:

• [✅] Fix a bug or typo in an existing algorithm?
• [x] Add or change doctests?
• [x] 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.
• [✅] All new Python files are placed inside an existing directory.
• [✅] All filenames are in all lowercase characters with no spaces or dashes.
• [✅] All functions and variable names follow Python naming conventions.
• [✅] All function parameters and return values are annotated with Python type hints.
• [✅] All functions have doctests that pass the automated testing.
• [✅] All new algorithms include at least one URL that points to Wikipedia or another similar explanation.
• [ ] If this pull request resolves one or more open issues then the description above includes the issue number(s) with a closing keyword: "Fixes #ISSUE-NUMBER".

Summary of Changes:

• Fixed issues with the Node and BinarySearchTree class implementations.
• Corrected traversal methods and node handling.
• Updated doctests to reflect accurate behavior and output.