feat(api): implement user authentication and registration endpoints

- Add main application logic in `api/src/main.rs` to initialize server, database, and services.
- Create authentication routes in `api/src/routes/auth.rs` for login, register, logout, and user info retrieval.
- Implement configuration route in `api/src/routes/config.rs` to expose application settings.
- Define application state management in `api/src/state.rs` to share user service and configuration.
- Set up Docker Compose configuration in `compose.yml` for backend, worker, and database services.
- Establish domain logic in `domain` crate with user entities, repositories, and services.
- Implement SQLite user repository in `infra/src/user_repository.rs` for user data persistence.
- Create database migration handling in `infra/src/db.rs` and session store in `infra/src/session_store.rs`.
- Add necessary dependencies and features in `Cargo.toml` files for both `domain` and `infra` crates.

api/src/state.rs

@@ -0,0 +1,36 @@
+//! Application State
+//!
+//! Holds shared state for the application.
+
+use axum::extract::FromRef;
+use std::sync::Arc;
+
+use crate::config::Config;
+use domain::UserService;
+
+#[derive(Clone)]
+pub struct AppState {
+    pub user_service: Arc<UserService>,
+    pub config: Arc<Config>,
+}
+
+impl AppState {
+    pub fn new(user_service: UserService, config: Config) -> Self {
+        Self {
+            user_service: Arc::new(user_service),
+            config: Arc::new(config),
+        }
+    }
+}
+
+impl FromRef<AppState> for Arc<UserService> {
+    fn from_ref(input: &AppState) -> Self {
+        input.user_service.clone()
+    }
+}
+
+impl FromRef<AppState> for Arc<Config> {
+    fn from_ref(input: &AppState) -> Self {
+        input.config.clone()
+    }
+}