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/api/auth-login.spec.ts

@@ -0,0 +1,39 @@
+import { test, expect } from '@playwright/test';
+import { createTestUser, registerUser } from '../fixtures';
+
+test.describe('POST /auth/login', () => {
+  test('logs in with valid credentials and returns token pair', async ({ request }) => {
+    const user = createTestUser();
+    await registerUser(request, user);
+
+    const res = await request.post('/auth/login', {
+      data: { phone: user.phone, password: user.password },
+    });
+
+    expect(res.status()).toBe(201);
+    const body = await res.json();
+    expect(body).toHaveProperty('accessToken');
+    expect(body).toHaveProperty('refreshToken');
+  });
+
+  test('rejects login with wrong password', async ({ request }) => {
+    const user = createTestUser();
+    await registerUser(request, user);
+
+    const res = await request.post('/auth/login', {
+      data: { phone: user.phone, password: 'WrongPassword!1' },
+    });
+
+    expect(res.ok()).toBeFalsy();
+    expect(res.status()).toBe(401);
+  });
+
+  test('rejects login with non-existent phone', async ({ request }) => {
+    const res = await request.post('/auth/login', {
+      data: { phone: '0900000001', password: 'Test@1234!' },
+    });
+
+    expect(res.ok()).toBeFalsy();
+    expect(res.status()).toBe(401);
+  });
+});