ref: refactor `KnightTour` implementation

[sozelfist]

Describe your change:

---

In this refactored version:

• I've organized the code into a KnightTour class to encapsulate related functions.
• Each method now belongs to the KnightTour class and operates on the class attributes.
• I've renamed some variables and methods for clarity.
• Magic numbers have been replaced with named constants.
• Error handling has been improved to raise more informative errors.
• The solve_knight_tour function now directly modifies the board rather than returning it, enhancing readability.
• I've added a check to ensure the board size is at least 1.
• The doctests remain intact and are still executed when running the script.

---

• [x] Refactor in an existing algorithm?
• [x] Documentation change?

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. To ease review, please open separate PRs for separate algorithms.
• [x] All new Python files are placed inside an existing directory.
• [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] All new algorithms include at least one URL that points to Wikipedia or another similar explanation.
• [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 #ISSUE-NUMBER".

[sozelfist]

Please have a look at this PR, @imSanko, @cclauss, @MaximSmolskiy

[sozelfist]

Can you help me ask for reviews from other code maintainers @imSanko or suggest making the code better to merge?

[sozelfist]

Requesting review: @cclauss, @MaximSmolskiy, and @imSanko.