Add user authentication and project persistence

[clencyc]

Description

Currently, projects are not saved. Add authentication so users can save their projects and access them across sessions.

Acceptance Criteria

• User signup/login with email
• JWT token-based auth
• Store projects in database (PostgreSQL)
• Each project has: name, description, created_date, modified_date, videos, edits
• List projects endpoint: GET /api/projects
• Save project endpoint: POST /api/projects
• Load project endpoint: GET /api/projects/{project_id}
• Delete project endpoint: DELETE /api/projects/{project_id}
• Projects private to user who created them
• Database schema migrations included
• Frontend shows "My Projects" page

Files to Create

• Backend: LiveEditBackend/auth.py - authentication logic
• Backend: LiveEditBackend/models.py - database models
• Frontend: pages/ProjectsPage.tsx - projects list UI
• Frontend: services/projectService.ts - project API calls

Tech Stack

• Backend: Flask-JWT-Extended
• Database: PostgreSQL with SQLAlchemy ORM
• Frontend: React Router for /projects page

Difficulty: Very Hard

Estimated time: 8-10 hours