refactor: Replace ApplicationController singleton with dependency injection

Co-authored-by: aider (gemini/gemini-2.5-pro) <aider@aider.chat>

src/main.cpp

@@ -1,11 +1,13 @@
 #include <QApplication>
 #include "MainWindow.h"
+#include "ApplicationController.h"
 
 int main(int argc, char *argv[])
 {
     QApplication app(argc, argv);
 
-    MainWindow window;
+    ApplicationController appController;
+    MainWindow window(&appController);
     window.show();
 
     return app.exec();