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/src/handlers.rs

@@ -0,0 +1,57 @@
+use axum::{
+    extract::{Query, State},
+    http::{HeaderMap, StatusCode},
+    response::Json,
+};
+use serde::Deserialize;
+use std::sync::Arc;
+
+use crate::{AppState, models::{LoginRequest, RegisterRequest, AuthResponse, ApiError}};
+
+#[derive(Deserialize)]
+pub struct VerifyQuery {
+    pub token: String,
+}
+
+pub async fn register(
+    State(state): State<Arc<AppState>>,
+    Json(request): Json<RegisterRequest>,
+) -> Result<Json<AuthResponse>, ApiError> {
+    let response = state.auth_service.register(request).await?;
+    Ok(Json(response))
+}
+
+pub async fn login(
+    State(state): State<Arc<AppState>>,
+    Json(request): Json<LoginRequest>,
+) -> Result<Json<AuthResponse>, ApiError> {
+    let response = state.auth_service.login(request).await?;
+    Ok(Json(response))
+}
+
+pub async fn verify_token(
+    State(state): State<Arc<AppState>>,
+    headers: HeaderMap,
+) -> Result<Json<serde_json::Value>, ApiError> {
+    // Try to get token from Authorization header
+    let token = if let Some(auth_header) = headers.get("authorization") {
+        let auth_str = auth_header
+            .to_str()
+            .map_err(|_| ApiError::BadRequest("Invalid authorization header".to_string()))?;
+        
+        if let Some(token) = auth_str.strip_prefix("Bearer ") {
+            token.to_string()
+        } else {
+            return Err(ApiError::BadRequest("Authorization header must start with 'Bearer '".to_string()));
+        }
+    } else {
+        return Err(ApiError::Unauthorized("Authorization header required".to_string()));
+    };
+
+    let user_info = state.auth_service.verify_token(&token).await?;
+    
+    Ok(Json(serde_json::json!({
+        "valid": true,
+        "user": user_info
+    })))
+}