feat: add Playwright configuration and initial e2e test for authentication

- Created Playwright configuration file to set up testing environment.
- Added a new e2e test for user authentication in login.spec.ts.
- Updated tsconfig.node.json to include playwright.config.ts.
- Enhanced vite.config.ts to include API proxying for backend integration.
- Added a placeholder for last run test results in .last-run.json.

frontend/playwright.config.ts

@@ -0,0 +1,22 @@
+import { defineConfig, devices } from '@playwright/test';
+
+const baseURL = process.env.PLAYWRIGHT_BASE_URL ?? 'http://localhost:8080';
+
+export default defineConfig({
+  testDir: './tests/e2e',
+  fullyParallel: true,
+  retries: process.env.CI ? 2 : 0,
+  reporter: [['list'], ['html', { outputFolder: 'playwright-report', open: 'never' }]],
+  use: {
+    baseURL,
+    trace: 'on-first-retry',
+    screenshot: 'only-on-failure',
+    video: 'retain-on-failure',
+  },
+  projects: [
+    {
+      name: 'chromium',
+      use: { ...devices['Desktop Chrome'] },
+    },
+  ],
+});