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/auth.spec.ts

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+import { test, expect } from '@playwright/test';
+
+test.describe('Authentication E2E Tests', () => {
+  test('should display login page', async ({ page }) => {
+    await page.goto('/login');
+    
+    // Check that login form is visible
+    await expect(page.getByRole('heading', { name: /login/i })).toBeVisible();
+    await expect(page.getByLabel(/email/i)).toBeVisible();
+    await expect(page.getByLabel(/password/i)).toBeVisible();
+    await expect(page.getByRole('button', { name: /login/i })).toBeVisible();
+  });
+
+  test('should display register page', async ({ page }) => {
+    await page.goto('/register');
+    
+    // Check that register form is visible
+    await expect(page.getByRole('heading', { name: /register/i })).toBeVisible();
+    await expect(page.getByLabel(/full name/i)).toBeVisible();
+    await expect(page.getByLabel(/email/i)).toBeVisible();
+    await expect(page.getByLabel(/password/i)).toBeVisible();
+    await expect(page.getByRole('button', { name: /register/i })).toBeVisible();
+  });
+
+  test('should navigate from login to register', async ({ page }) => {
+    await page.goto('/login');
+    
+    // Click on register link
+    await page.getByRole('link', { name: /register/i }).click();
+    
+    // Should be on register page
+    await expect(page).toHaveURL(/.*register/);
+    await expect(page.getByRole('heading', { name: /register/i })).toBeVisible();
+  });
+});
+
+test.describe('Event List E2E Tests', () => {
+  test('should display events page', async ({ page }) => {
+    await page.goto('/events');
+    
+    // Check that events list is visible
+    await expect(page.getByRole('heading', { name: /events/i })).toBeVisible();
+    
+    // Check for filters
+    await expect(page.getByRole('combobox').first()).toBeVisible();
+  });
+});
+
+test.describe('Navigation E2E Tests', () => {
+  test('should navigate through main pages', async ({ page }) => {
+    // Start at home
+    await page.goto('/');
+    
+    // Navigate to events
+    await page.getByRole('link', { name: /events/i }).first().click();
+    await expect(page).toHaveURL(/.*events/);
+    
+    // Navigate to login
+    await page.getByRole('link', { name: /login/i }).click();
+    await expect(page).toHaveURL(/.*login/);
+  });
+});

tests/integration/e2e/playwright.config.ts

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+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,
+  },
+});