feat: flutter ui integration

ui/flutter/lib/pages/root/root_controller.dart

@@ -0,0 +1,20 @@
+import 'package:get/get.dart';
+
+class RootController extends GetxController {
+  //TODO: Implement RootController
+
+  final count = 0.obs;
+  @override
+  void onInit() {
+    super.onInit();
+  }
+
+  @override
+  void onReady() {
+    super.onReady();
+  }
+
+  @override
+  void onClose() {}
+  void increment() => count.value++;
+}