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

tests/integration/e2e/playwright.config.ts

@@ -0,0 +1,25 @@
+import { defineConfig, devices } from '@playwright/test';
+
+export default defineConfig({
+  testDir: '.',
+  fullyParallel: true,
+  forbidOnly: !!process.env.CI,
+  retries: process.env.CI ? 2 : 0,
+  workers: process.env.CI ? 1 : undefined,
+  reporter: 'list',
+  use: {
+    baseURL: 'http://localhost:3000',
+    trace: 'on-first-retry',
+  },
+  projects: [
+    {
+      name: 'chromium',
+      use: { ...devices['Desktop Chrome'] },
+    },
+  ],
+  webServer: {
+    command: 'cd ../../frontend && npm run dev',
+    url: 'http://localhost:3000',
+    reuseExistingServer: !process.env.CI,
+  },
+});