feat: add sponsor badge UI integration

[srinidhi-2006-bit]

Summary

Added a reusable SponsorBadge component and integrated sponsor badge support into leaderboard and public profile UI.

Closes #1055

Type of Change

• Bug fix
• New feature
• Documentation update
• Refactor / code cleanup

Changes Made

• Added reusable SponsorBadge component
• Added sponsor badge rendering in leaderboard entries
• Added sponsor badge rendering in public profile pages
• Added accessible tooltip and aria-label support
• Added temporary sponsor mapping for UI testing
• Extended PublicProfileData type with sponsor support

How to Test

Steps for the reviewer to verify this works:

1. Run:

   npm run dev

2. Open:

   /leaderboard
   

3. Verify sponsor badge appears beside sponsor usernames

4. Open:

   /u/priyanshu-byte-coder
   

5. Verify sponsor badge appears beside profile username

6. Run:

   npm run lint
   npm run type-check

7. Verify there are no lint or TypeScript errors

Screenshots (if UI change)

Added sponsor badge UI beside usernames in leaderboard and public profile pages.

Checklist

• Linked issue in summary
• npm run lint passes locally
• No TypeScript errors (npm run type-check)
• Self-reviewed the diff
• Added/updated tests if applicable

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[github-actions]

GSSoC Label Checklist 🏷️

@Priyanshu-byte-coder — please apply the appropriate labels before merging:

Difficulty (pick one):

• level:beginner — 20 pts
• level:intermediate — 35 pts
• level:advanced — 55 pts
• level:critical — 80 pts

Quality (optional):

• quality:clean — ×1.2 multiplier
• quality:exceptional — ×1.5 multiplier

Validation (required to score):

• gssoc:approved — counts for points
• gssoc:invalid / gssoc:spam / gssoc:ai-slop — does not score

Type labels (type:*) are auto-detected from files and title. Review and adjust if needed.
Points formula: (difficulty × quality_multiplier) + type_bonus

[srinidhi-2006-bit]

Hi @Priyanshu-byte-coder,

Implemented the sponsor badge UI integration for leaderboard and public profile pages.

Verified locally that:

• npm run lint passes
• npm run type-check passes

The PR includes:

• Reusable SponsorBadge component
• Sponsor badge rendering in leaderboard entries
• Sponsor badge rendering in public profiles
• Accessibility support with tooltip and aria-labels

Could you please review the PR and add the gssoc:approved label if everything looks good?

Thank you!