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

❌ Patch coverage is 58.33333% with 10 lines in your changes missing coverage. Please review.
✅ Project coverage is 77.08%. Comparing base (c0ca704) to head (f7b63d6).

Files with missing lines	Patch %	Lines
...java/com/thealgorithms/others/HappyNumbersSeq.java	58.33%	10 Missing ⚠️

Additional details and impacted files

@@             Coverage Diff              @@
##             master    #6644      +/-   ##
============================================
- Coverage     77.10%   77.08%   -0.02%     
- Complexity     6110     6119       +9     
============================================
  Files           719      720       +1     
  Lines         20437    20461      +24     
  Branches       3952     3957       +5     
============================================
+ Hits          15758    15773      +15     
- Misses         4080     4090      +10     
+ Partials        599      598       -1     

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[DenizAltunkapan]

@Hardvan Please resolve the conflicts in this branch so i can start the review

[Hardvan]

@DenizAltunkapan Done, I have resolved the conflicts