feat(e2e): add Playwright E2E testing infrastructure and critical path tests

Set up Playwright with dual-project config (API + Web), auth test fixtures,
16 E2E tests covering registration, login, profile, token refresh, and
homepage rendering. Added GitHub Actions CI workflow for automated E2E runs.

Co-Authored-By: Paperclip <noreply@paperclip.ing>

e2e/web/homepage.spec.ts

@@ -0,0 +1,39 @@
+import { test, expect } from '@playwright/test';
+
+test.describe('Homepage', () => {
+  test('loads and displays platform title', async ({ page }) => {
+    await page.goto('/');
+
+    await expect(page.locator('h1')).toContainText('GoodGo Platform');
+    await expect(page.locator('p')).toContainText('Vietnam Real Estate Platform');
+  });
+
+  test('has correct page title', async ({ page }) => {
+    await page.goto('/');
+
+    await expect(page).toHaveTitle(/GoodGo/i);
+  });
+
+  test('renders without console errors', async ({ page }) => {
+    const errors: string[] = [];
+    page.on('console', (msg) => {
+      if (msg.type() === 'error') errors.push(msg.text());
+    });
+
+    await page.goto('/');
+    await page.waitForLoadState('networkidle');
+
+    expect(errors).toHaveLength(0);
+  });
+
+  test('is responsive — mobile viewport', async ({ page }) => {
+    await page.setViewportSize({ width: 375, height: 667 });
+    await page.goto('/');
+
+    const main = page.locator('main');
+    await expect(main).toBeVisible();
+
+    const h1 = page.locator('h1');
+    await expect(h1).toBeVisible();
+  });
+});