Enhance auth flows and improve e2e test reliability

- Remove redundant `'use client'` directives in auth pages to streamline code.
- Refine Playwright config: adjust worker limits and add video recording for failed tests.
- Improve session management in e2e tests with isolated state clearing, console log collection, and detailed failure attachments.
- Update API client: better handle auth routes, ensure safe token refresh, and prevent unnecessary redirects.

frontend/src/app/(auth)/login/page.tsx

@@ -1,5 +1,3 @@
-'use client';
-
 import dynamic from 'next/dynamic';
 
 // Code-split LoginForm - heavy with react-hook-form + validation

frontend/src/app/(auth)/password-reset/page.tsx

@@ -3,8 +3,6 @@
  * Users enter their email to receive reset instructions
  */
 
-'use client';
-
 import dynamic from 'next/dynamic';
 
 // Code-split PasswordResetRequestForm

frontend/src/app/(auth)/register/page.tsx

@@ -1,5 +1,3 @@
-'use client';
-
 import dynamic from 'next/dynamic';
 
 // Code-split RegisterForm (313 lines)