feat: Add automated testing with Vitest and Playwright

- Install Vitest (integration tests for API routes) and Playwright (E2E tests)
- Add vitest.config.ts, playwright.config.ts, src/test/setup.ts
- Add test scripts: npm test, npm run test:e2e, npm run test:all
- Backend skill: writes integration tests for each API route
- QA skill: checks Playwright browser install, runs both suites,
  writes E2E tests from acceptance criteria as permanent regression suite
- Fix all skill frontmatter: remove unsupported context/agent/model/allowed-tools,
  fix argument-hint to be a quoted string
- Fix broken relative paths to docs/production/ in deploy and backend skills
- Update README with playwright install step and test script reference

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

package.json

@@ -7,7 +7,12 @@
     "dev": "next dev",
     "build": "next build",
     "start": "next start",
-    "lint": "next lint"
+    "lint": "next lint",
+    "test": "vitest run",
+    "test:watch": "vitest",
+    "test:e2e": "playwright test",
+    "test:e2e:ui": "playwright test --ui",
+    "test:all": "vitest run && playwright test"
   },
   "dependencies": {
     "@hookform/resolvers": "^5.2.2",
@@ -46,14 +51,21 @@
     "zod": "^4.3.5"
   },
   "devDependencies": {
+    "@playwright/test": "^1.58.2",
+    "@testing-library/jest-dom": "^6.9.1",
+    "@testing-library/react": "^16.3.2",
     "@types/node": "^20",
     "@types/react": "^19",
     "@types/react-dom": "^19",
+    "@vitejs/plugin-react": "^6.0.1",
+    "@vitest/ui": "^4.1.2",
     "autoprefixer": "^10.0.1",
     "eslint": "^9",
     "eslint-config-next": "16.1.1",
+    "jsdom": "^29.0.1",
     "postcss": "^8",
     "tailwindcss": "^3.4.1",
-    "typescript": "^5"
+    "typescript": "^5",
+    "vitest": "^4.1.2"
   }
 }