Disable header bar when not using GNOME Shell. (#68452)

Fixes https://github.com/flutter/flutter/issues/68253

packages/flutter_tools/templates/app/linux.tmpl/my_application.cc.tmpl

 #include "my_application.h"
 
 #include <flutter_linux/flutter_linux.h>
+#ifdef GDK_WINDOWING_X11
+#include <gdk/gdkx.h>
+#endif
 
 #include "flutter/generated_plugin_registrant.h"
 
@@ -14,11 +17,35 @@ G_DEFINE_TYPE(MyApplication, my_application, GTK_TYPE_APPLICATION)
 static void my_application_activate(GApplication* application) {
   GtkWindow* window =
       GTK_WINDOW(gtk_application_window_new(GTK_APPLICATION(application)));
-  GtkHeaderBar *header_bar = GTK_HEADER_BAR(gtk_header_bar_new());
-  gtk_widget_show(GTK_WIDGET(header_bar));
-  gtk_header_bar_set_title(header_bar, "{{projectName}}");
-  gtk_header_bar_set_show_close_button(header_bar, TRUE);
-  gtk_window_set_titlebar(window, GTK_WIDGET(header_bar));
+
+  // Use a header bar when running in GNOME as this is the common style used
+  // by applications and is the setup most users will be using (e.g. Ubuntu
+  // desktop).
+  // If running on X and not using GNOME then just use a traditional title bar
+  // in case the window manager does more exotic layout, e.g. tiling.
+  // If running on Wayland assume the header bar will work (may need changing
+  // if future cases occur).
+  gboolean use_header_bar = TRUE;
+#ifdef GDK_WINDOWING_X11
+  GdkScreen *screen = gtk_window_get_screen(window);
+  if (GDK_IS_X11_SCREEN(screen)) {
+     const gchar* wm_name = gdk_x11_screen_get_window_manager_name(screen);
+     if (g_strcmp0(wm_name, "GNOME Shell") != 0) {
+       use_header_bar = FALSE;
+     }
+  }
+#endif
+  if (use_header_bar) {
+    GtkHeaderBar *header_bar = GTK_HEADER_BAR(gtk_header_bar_new());
+    gtk_widget_show(GTK_WIDGET(header_bar));
+    gtk_header_bar_set_title(header_bar, "{{projectName}}");
+    gtk_header_bar_set_show_close_button(header_bar, TRUE);
+    gtk_window_set_titlebar(window, GTK_WIDGET(header_bar));
+  }
+  else {
+    gtk_window_set_title(window, "{{projectName}}");
+  }
+
   gtk_window_set_default_size(window, 1280, 720);
   gtk_widget_show(GTK_WIDGET(window));