feat: Add "CENTURION" Gamification Badge to User Profile #332

[yashvi-3106]

Description

This PR implements the new "CENTURION" Gamification Badge for user profiles. The badge is awarded dynamically based on a user's total solved problems count.

Linked Issue

Fixes #332

Changes Made

• frontend/js/user/badges.js:
  • Registered CENTURION to the ALL_BADGES configuration list.
  • Implemented the badge unlock condition in loadBadges() to check the user's latest snapshot for a grand total of $\ge 100$ solved problems across all difficulties.
• frontend/user.html:
  • Added CSS style declarations for .badge-centurion implementing a premium neon orange/amber theme (#ff9f1c).

Type of Change

• Bug fix
• New feature
• UI/Visual update
• Documentation update
• Refactor

Testing

• Tested locally
• Tested on mobile viewport (if applicable)
• No console errors introduced

Checklist

• My code follows the project's coding style
• I have formatted my code locally by running npx prettier --write . before submitting
• I am submitting my PR from a dedicated feature/* branch, not the main branch
• I have performed a self-review of my code
• My changes generate no new warnings or errors
• I have updated documentation if required
• I have linked the relevant issue

Screenshots / Screen Recording

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