Integrate authentication (Google OAuth + Email OTP) with frontend

## Integrate authentication (Google OAuth + Email OTP) with frontend

### Description
Hook up the Flutter frontend to the existing backend auth endpoints — both Google OAuth and Email OTP.

### Tasks
- [ ] Email login: call `POST /api/login/email`, build OTP screen, call `POST /api/login/verify-otp`
- [ ] Google login: trigger `GET /api/login/oauth` via `flutter_web_auth_2`, handle `amingo://auth-callback?token=...` redirect from `GET /api/login/callback`
- [ ] Navigate to display name / home screen after successful login
- [ ] Handle errors: expired/incorrect OTP, canceled OAuth, network failure

Start by locating the Flutter frontend's authentication entry point and reviewing the existing POST /api/login/email, POST /api/login/verify-otp, GET /api/login/oauth, and GET /api/login/callback flows. Done means both email OTP and Google OAuth reach the display name or home screen, with expired or incorrect OTP, canceled OAuth, and network failures handled.

Escrita pelo modelo de indexação a partir do texto da issue.