Implement complete full-stack authentication system

- Restructure project with separate frontend/backend architecture
- Create dedicated backend with Axum, SQLite, JWT authentication
- Implement real API endpoints for register/login/verify
- Update frontend to use HTTP requests instead of mock auth
- Add bcrypt password hashing and secure token generation
- Separate Cargo.toml files for frontend and backend builds
- Fix Trunk compilation by isolating WASM-incompatible dependencies
- Create demo user in database for easy testing
- Both servers running: frontend (8081), backend (3000)

🤖 Generated with [Claude Code](https://claude.ai/code)

Co-Authored-By: Claude <noreply@anthropic.com>

backend/Cargo.toml

@@ -0,0 +1,29 @@
+[package]
+name = "calendar-backend"
+version = "0.1.0"
+edition = "2021"
+
+[[bin]]
+name = "backend"
+path = "src/main.rs"
+
+[dependencies]
+# Backend authentication dependencies
+sqlx = { version = "0.7", features = ["runtime-tokio-rustls", "sqlite", "chrono", "uuid", "migrate"] }
+bcrypt = "0.15"
+jsonwebtoken = "9.0"
+tokio = { version = "1.0", features = ["full"] }
+axum = { version = "0.7", features = ["json"] }
+tower = "0.4"
+tower-http = { version = "0.5", features = ["cors"] }
+hyper = { version = "1.0", features = ["full"] }
+
+# Shared dependencies
+serde = { version = "1.0", features = ["derive"] }
+serde_json = "1.0"
+chrono = { version = "0.4", features = ["serde"] }
+uuid = { version = "1.0", features = ["v4", "serde"] }
+anyhow = "1.0"
+
+[dev-dependencies]
+tokio = { version = "1.0", features = ["macros", "rt"] }