refactor: Enhance docs, code, add tests in HappyNumbersSeq

[Hardvan]

• I have read CONTRIBUTING.md.
• This pull request is all my own work -- I have not plagiarized it.
• All filenames are in PascalCase.
• All functions and variable names follow Java naming conventions.
• All new algorithms have a URL in their comments that points to Wikipedia or other similar explanations.
• 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.
✅ Project coverage is 75.77%. Comparing base (a0b6c52) to head (dc104b2).

Additional details and impacted files

@@             Coverage Diff              @@
##             master    #6644      +/-   ##
============================================
+ Coverage     75.74%   75.77%   +0.03%     
- Complexity     5765     5774       +9     
============================================
  Files           701      701              
  Lines         19757    19764       +7     
  Branches       3831     3833       +2     
============================================
+ Hits          14964    14977      +13     
+ Misses         4214     4208       -6     
  Partials        579      579              

☔ View full report in Codecov by Sentry.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.