test(web): add middleware + i18n + messages test suites (GOO-60)

Cover frontend middleware auth/locale logic, i18n config/routing/request/navigation,
and vi/en message parity — 91 new tests across 6 files.

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

apps/api/package.json

@@ -9,6 +9,7 @@
     "start:prod": "node dist/main",
     "lint": "eslint src/",
     "test": "vitest run",
+    "test:coverage": "vitest run --coverage",
     "test:integration": "vitest run --config vitest.integration.config.ts",
     "typecheck": "tsc --noEmit"
   },
@@ -16,6 +17,7 @@
     "@anthropic-ai/sdk": "^0.89.0",
     "@aws-sdk/client-s3": "^3.1026.0",
     "@aws-sdk/s3-request-presigner": "^3.1026.0",
+    "@goodgo/ai-contract": "workspace:*",
     "@goodgo/mcp-servers": "workspace:*",
     "@nest-lab/throttler-storage-redis": "^1.2.0",
     "@nestjs/bullmq": "^11.0.4",
@@ -84,6 +86,7 @@
     "@types/qrcode": "^1.5.6",
     "@types/sanitize-html": "^2.16.1",
     "@types/supertest": "^7.2.0",
+    "@vitest/coverage-v8": "^4.1.3",
     "prisma": "^7.7.0",
     "supertest": "^7.2.2",
     "typescript": "^6.0.2",