### Tested versions

v4.2.stable.official [46dc27791]

### System information

Windows 11- Godot v4.2.stable.official [46dc27791] - Vulkan (Forward+)

### Issue description

When I switch picker mode the next time I open it should be the pick mode I selected last time but it's not

https://github.com/godotengine/godot/assets/46812028/522c8b55-14cf-4781-963f-a465a03c9432



### Steps to reproduce

Toggle a picker mode off and on again

### Minimal reproduction project (MRP)

N/A
pick_main_scene->set_meta("from_native", p_from_native); 
	String main_scene = GLOBAL_GET("application/run/main_scene");
	if (main_scene.is_empty()) {
		current_menu_option = -1;
		pick_main_scene->set_text(TTR("No main scene has ever been defined, select one?\nYou can change it later in \"Project Settings\" under the 'application' category."));
		pick_main_scene->popup_centered();
		if (editor_data.get_edited_scene_root()) {
			select_current_scene_button->set_disabled(false);
			select_current_scene_button->grab_focus();
		} else {
			select_current_scene_button->set_disabled(true);
		}
		return false;
	}
	if (!FileAccess::exists(main_scene)) {
		current_menu_option = -1;
		pick_main_scene->set_text(vformat(TTR("Selected scene '%s' does not exist, select a valid one?\nYou can change it later in \"Project Settings\" under the 'application' category."), main_scene));
		pick_main_scene->popup_centered();
		return false;
	}
	if (ResourceLoader::get_resource_type(main_scene) != "PackedScene") {
		current_menu_option = -1;
		pick_main_scene->set_text(vformat(TTR("Selected scene '%s' is not a scene file, select a valid one?\nYou can change it later in \"Project Settings\" under the 'application' category."), main_scene));
		pick_main_scene->popup_centered();
		return false;
	}
	return true;
}
void EditorNode::_immediate_dialog_confirmed() {