test(public): add regression coverage for public route registration

[Ridanshi]

Closes #309

Summary

Adds focused regression coverage for the public profile routes involved in #309 to ensure runtime Fastify route-registration failures do not reappear.

The underlying implementation in apps/backend/src/routes/public.ts is already fixed on latest upstream/main, so this PR intentionally avoids modifying route logic and instead protects against future regressions through targeted test coverage.

Covered routes:

• GET /api/public/:username
• GET /api/public/:username/card/:cardId
• GET /api/public/:username/qr

Tests Added

Added focused regression tests verifying:

• public profile route returns 200 OK
• public shared-card route returns 200 OK
• routes do not trigger runtime Fastify registration errors
• QR endpoint behavior remains unchanged

Notes

• No API contract changes
• No route implementation changes
• No unrelated refactors
• Only focused regression coverage added for the already-fixed production issue

Verification

node_modules\.bin\vitest.CMD run src\__tests__\public.test.ts

[Ridanshi]

PR #352 addresses issue #309 by adding focused regression coverage for the affected public profile routes.

The underlying nested app.get() registration problem is already fixed on latest upstream/main, so this PR intentionally avoids unnecessary route changes and instead protects against regressions through targeted tests.

Covered routes:

• GET /api/public/:username
• GET /api/public/:username/card/:cardId
• GET /api/public/:username/qr

The new tests verify:

• affected routes return 200 OK
• runtime Fastify route-registration errors do not reappear
• QR endpoint behavior remains unchanged

No API contract changes or unrelated refactors were introduced.