feat: wire relay API with dependency injection

- split settings module into per-struct files
- add DatabaseSettings with default in-memory SQLite path
- implement RelayApi struct with GET /relays and POST
  /relays/{id}/toggle
- wire create_relay_controller and create_label_repository into
  Application::build() with mock/real selection via cfg!(test) || CI
- register RelayApi in OpenApiService alongside existing APIs

backend/tests/sqlite_repository_functional_test.rs

@@ -427,7 +427,10 @@ async fn test_repository_error_handling() {
 
     // Test with invalid relay ID (should be caught by domain validation)
     let invalid_relay_id = RelayId::new(9); // This will fail validation
-    assert!(invalid_relay_id.is_err(), "Invalid relay ID should fail validation");
+    assert!(
+        invalid_relay_id.is_err(),
+        "Invalid relay ID should fail validation"
+    );
 
     // Test with invalid label (should be caught by domain validation)
     let invalid_label = RelayLabel::new("".to_string()); // Empty label
@@ -444,7 +447,7 @@ async fn test_concurrent_operations_are_thread_safe() {
     // Since SqliteRelayLabelRepository doesn't implement Clone, we'll test
     // sequential operations which still verify the repository handles
     // multiple operations correctly
-    
+
     // Save multiple labels sequentially
     let relay_id1 = RelayId::new(1).expect("Valid relay ID");
     let label1 = RelayLabel::new("Task1".to_string()).expect("Valid label");
@@ -470,4 +473,4 @@ async fn test_concurrent_operations_are_thread_safe() {
         .await
         .expect("get_all_labels should succeed");
     assert_eq!(all_labels.len(), 3, "Should have all 3 labels");
-}
+}