refactor: `BoardPath`

[alxkm]

Class cleanup. Readability improvements. Added tests.

• [x] I have read CONTRIBUTING.md.
• [x] This pull request is all my own work -- I have not plagiarized it.
• [x] All filenames are in PascalCase.
• [x] All functions and variable names follow Java naming conventions.
• [x] All new algorithms have a URL in their comments that points to Wikipedia or other similar explanations.
• [x] All new code is formatted with clang-format -i --style=file path/to/your/file.java

[codecov-commenter]

Codecov Report

All modified and coverable lines are covered by tests :white_check_mark:

Project coverage is 50.97%. Comparing base (c5b7281) to head (05503b9).

Additional details and impacted files

```diff @@ Coverage Diff @@ ## master #5431 +/- ## ============================================ + Coverage 50.78% 50.97% +0.18% - Complexity 3138 3152 +14 ============================================ Files 523 523 Lines 15108 15104 -4 Branches 2874 2874 ============================================ + Hits 7673 7699 +26 + Misses 7114 7084 -30 Partials 321 321 ```

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