test: implement comprehensive test strategy

- Add Playwright for E2E testing with auth.spec.ts
- Add dialog component tests (8 test cases)
- Add sidebar component tests (11 test cases)
- Add login page integration tests (11 test cases)
- Add dashboard page tests (12 test cases)
- Update package.json with e2e test scripts
- Configure Playwright for Chromium and Firefox
- Test coverage for UI interactions, auth flows, and navigation

admin-web/package.json

@@ -9,7 +9,11 @@
     "lint": "eslint",
     "test": "vitest run",
     "test:watch": "vitest",
-    "test:coverage": "vitest run --coverage"
+    "test:coverage": "vitest run --coverage",
+    "test:e2e": "playwright test",
+    "test:e2e:ui": "playwright test --ui",
+    "test:e2e:headed": "playwright test --headed",
+    "test:all": "npm run test && npm run test:e2e"
   },
   "dependencies": {
     "@supabase/ssr": "^0.9.0",
@@ -24,6 +28,7 @@
     "tailwind-merge": "^3.5.0"
   },
   "devDependencies": {
+    "@playwright/test": "^1.58.2",
     "@tailwindcss/postcss": "^4",
     "@testing-library/jest-dom": "^6.9.1",
     "@testing-library/react": "^16.3.2",