refactor: Replace ApplicationController singleton with dependency injection

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

src/ApplicationController.h

@@ -12,7 +12,8 @@ class ApplicationController : public QObject
 {
     Q_OBJECT
 public:
-    static ApplicationController* instance();
+    explicit ApplicationController(QObject *parent = nullptr);
+    ~ApplicationController();
 
     void setMainWindow(MainWindow* mainWindow);
     Document* document() const;
@@ -33,8 +34,6 @@ signals:
     void currentFileChanged(const QString& path);
 
 private:
-    explicit ApplicationController(QObject *parent = nullptr);
-    ~ApplicationController();
     ApplicationController(const ApplicationController&) = delete;
     ApplicationController& operator=(const ApplicationController&) = delete;