feat: implement BALANCED badge dynamically on user profiles

[Yashaswini-K-P]

Description

Implemented a new dynamic BALANCED badge on user profile pages to reward students who maintain an even distribution of problem solving across difficulties (at least 5 solved in Easy, Medium, and Hard, with the gap between highest and lowest counts being within 5% of the highest count).

Linked Issue

Fixes #336

Changes Made

• Added the BALANCED badge definition to the ALL_BADGES array in frontend/js/user/badges.js.
• Implemented evaluation logic in loadBadges() to verify minimum counts and ensure the spread between difficulties satisfies the 5% threshold condition.
• Added a distinct teal/cyan theme CSS style class (.badge-balanced) in frontend/user.html.

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

[github-actions]

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[jagdish-15]

/format

[github-actions]

All done! 💅 I've run Prettier and pushed the formatting fixes to this PR.

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