AUTH-002: User registration — sign-up form with email verification

## Overview
Implement the user registration flow. New users can create an account with email, password, and display name. A verification email is sent on registration.

## Acceptance Criteria
- [ ] Registration form with name, email, password, and confirm-password fields
- [ ] Client-side validation before submission
- [ ] Verification email sent via transactional email service
- [ ] User is logged in automatically after verifying their email
- [ ] Duplicate email check returns a clear error

## Depends On
- #5 (AUTH-001 — login flow and session management)

Start by reading #5, AUTH-001, to understand the existing login flow and session management before planning registration. Then use the acceptance criteria as the completion checklist: form validation, duplicate-email errors, verification email delivery, and automatic login after email verification.

Written by the indexing model from the issue text.