Refactor: untangle framework library from todo example

The codebase is now split into two clear layers:

Framework library (src/):
- lib.rs — public API surface, re-exports all framework types
- signal.rs — SignalOpts, Signal, SignalStore, mangle/global/client_only helpers
- query.rs — Query trait, CacheKey, query_one!/query_all! macros
  (macro paths updated from $crate::framework::* to $crate::*)
- context.rs — RenderContext, ComponentTree, ComponentNode
- connection.rs — ConnectionManager, SubscriptionRegistry, ConnectionState
- sse.rs — format_patch_elements, format_patch_signals
- server.rs — AppState, SharedState, sse_handler (pure framework plumbing)

Todo example (examples/todo/):
- main.rs — SQLite setup, seeding, server bootstrap
- app.rs — router, document_shell, resolve_and_render, render_page,
  action_then_render, and all HTTP handlers
- queries.rs — Todo model, ListTodos/GetTodo queries, mutation helpers
- todo_list.rs — TodoList page component
- about.rs — About page component

Run the example independently with: cargo run --example todo

https://claude.ai/code/session_01JThiQbp3Bn9J1VhBpRuz4u

examples/todo/main.rs

@@ -0,0 +1,64 @@
+mod app;
+mod queries;
+mod todo_list;
+mod about;
+
+use livevue_rs::{AppState, ConnectionManager, SubscriptionRegistry};
+use std::sync::Arc;
+
+#[tokio::main]
+async fn main() -> anyhow::Result<()> {
+    // -----------------------------------------------------------------------
+    // Database setup
+    // -----------------------------------------------------------------------
+
+    // SQLite with create-if-missing. In-memory `:memory:` also works for dev.
+    let db = sqlx::SqlitePool::connect("sqlite:todo.db?mode=rwc").await?;
+
+    // Run migrations inline (no migration files needed for v0).
+    sqlx::query(
+        "CREATE TABLE IF NOT EXISTS todos (
+            id INTEGER PRIMARY KEY AUTOINCREMENT,
+            title TEXT NOT NULL,
+            completed BOOLEAN NOT NULL DEFAULT FALSE
+        )",
+    )
+    .execute(&db)
+    .await?;
+
+    // Seed a few todos if the table is empty (nice for first run)
+    let count: (i64,) = sqlx::query_as("SELECT COUNT(*) FROM todos")
+        .fetch_one(&db)
+        .await?;
+    if count.0 == 0 {
+        for title in &["Learn Rust", "Build LiveVue.rs", "Ship v0"] {
+            sqlx::query("INSERT INTO todos (title, completed) VALUES (?, false)")
+                .bind(title)
+                .execute(&db)
+                .await?;
+        }
+    }
+
+    // -----------------------------------------------------------------------
+    // Application state
+    // -----------------------------------------------------------------------
+
+    let state = Arc::new(AppState {
+        db,
+        connections: ConnectionManager::new(),
+        subscriptions: SubscriptionRegistry::new(),
+    });
+
+    // -----------------------------------------------------------------------
+    // Server
+    // -----------------------------------------------------------------------
+
+    let app = app::router(state);
+
+    let listener = tokio::net::TcpListener::bind("0.0.0.0:3000").await?;
+    println!("Todo example listening on http://localhost:3000");
+
+    axum::serve(listener, app).await?;
+
+    Ok(())
+}