feat: implement Hangman game UI and gameplay logic with DOM interaction

[DinethShakya23]

Summary

Added a fully functional Hangman game feature that allows users to guess words letter by letter with real time feedback.

• Displays word progress using underscores for unguessed letters.
• Tracks incorrect guesses and limits the number of attempts.
• Tracking remaining guesses and synchronizing hangman drawing with wrong guesses.
• Includes win/lose messages and an option to restart the game.

Checklist

• Linked issue (New Project: 2-Player Hangman Game #126 )
• Ran locally without console errors
• Focused scope (kept PR small)
• Updated docs or TODO comments if needed

Screenshots

Additional Notes

• added the game to the home page (by updating projects.json file)
• refactor main index.html for proper code indentation/formatting (no code changes)

[vercel]

@DinethShakya23 is attempting to deploy a commit to the hrishikesh-dalal's projects Team on Vercel.

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