Auth with passwords + Playwright E2E tests + PostHog analytics

- bcrypt password hashing in auth (register, login, change-password)
- Login/register pages with password fields
- Profile update + OAuth placeholder endpoints
- Playwright test suite: auth, pages, API (3 test files)
- PostHog Docker analytics on :8010

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

playwright.config.ts

@@ -0,0 +1,16 @@
+import { defineConfig } from '@playwright/test';
+
+export default defineConfig({
+    testDir: './tests',
+    timeout: 30000,
+    use: {
+        baseURL: 'http://localhost:3001',
+        headless: true,
+        screenshot: 'only-on-failure',
+    },
+    projects: [{ name: 'chromium', use: { browserName: 'chromium' } }],
+    reporter: [
+        ['list'],
+        ['json', { outputFile: '/opt/task-team/test-results.json' }],
+    ],
+});