backend: use structured response modeling in public profile endpoint

[Harxhit]

Summary

Added dedicated TypeScript interfaces for all public profile and card responses in apps/backend/src/routes/public.ts. This provides full compile-time type safety and encourages consistent API contracts across the public endpoints.

Closes #21

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Type of Change

• Refactor (no functional change)
• Documentation

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What Changed

• Created four new type interfaces in public.ts:
  • PublicProfileLink
  • UsernamePublicProfileResponse
  • CardPublicProfileResponse
  • UsernameCardPublicProfileResponse
• Updated the three public routes to return properly typed response objects:
  • GET /:username (public profile)
  • GET /card/:cardId (direct shared card)
  • GET /:username/card/:cardId (username + card view)
• Added/improved JSDoc comments with clear API documentation for all three endpoints.

No functional changes — only improved type safety and documentation.

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Checklist

• My code follows the project's coding style (pnpm -r run lint passes).
• TypeScript compiles without errors (pnpm -r run typecheck).
• I have added or updated tests for the changes I made.
• All tests pass locally (pnpm -r run test).
• I have updated documentation where necessary.
• No new console.log or debug statements left in the code.
• Breaking changes are documented in this PR description.