Add complete integration test suite

Backend Integration Tests:
- Create IntegrationTestBase class with WebApplicationFactory
- AuthIntegrationTests: Registration, login, validation tests (5 tests)
- EventsIntegrationTests: CRUD operations, authorization tests (8 tests)

Frontend-Backend Integration (E2E):
- Install Playwright with Chromium
- Create playwright.config.ts with configuration
- Auth E2E tests: login/register page visibility, navigation
- Event List E2E tests: page display
- Navigation E2E tests: main page navigation flow

Total Integration Tests:
- Backend: 13 tests covering Auth and Events
- E2E: 6 tests covering UI flows

package.json

@@ -1,5 +1,8 @@
 {
   "devDependencies": {
-    "jest-environment-jsdom": "^30.3.0"
+    "@playwright/test": "^1.59.1",
+    "@types/supertest": "^7.2.0",
+    "jest-environment-jsdom": "^30.3.0",
+    "supertest": "^7.2.2"
   }
 }