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>

tests/auth.spec.ts

@@ -0,0 +1,32 @@
+import { test, expect } from '@playwright/test';
+
+test.describe('Auth Flow', () => {
+    const email = `test-${Date.now()}@test.cz`;
+    
+    test('register page loads', async ({ page }) => {
+        await page.goto('/register');
+        await expect(page).toHaveTitle(/Task Team/);
+    });
+
+    test('login page loads', async ({ page }) => {
+        await page.goto('/login');
+        await expect(page.locator('input[type="email"]')).toBeVisible();
+    });
+
+    test('register new user', async ({ page }) => {
+        await page.goto('/register');
+        // Name is the first text input (autoFocus), email is type=email
+        await page.locator('input[type="text"]').first().fill('Test User');
+        await page.locator('input[type="email"]').fill(email);
+        await page.locator('button[type="submit"]').click();
+        await page.waitForTimeout(2000);
+        // Should redirect to tasks or show success
+    });
+
+    test('login existing user', async ({ page }) => {
+        await page.goto('/login');
+        await page.fill('input[type="email"]', email);
+        await page.locator('button[type="submit"]').click();
+        await page.waitForTimeout(2000);
+    });
+});