### 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
if (DisplayServer::get_singleton()->window_can_draw()) {
				ProjectSettings::get_singleton()->save();
			}
			_titlebar_resized();
			
			CanvasItemEditor::ThemePreviewMode theme_preview_mode = (CanvasItemEditor::ThemePreviewMode)(int)EditorSettings::get_singleton()->get_project_metadata("2d_editor", "theme_preview", CanvasItemEditor::THEME_PREVIEW_PROJECT);
			update_preview_themes(theme_preview_mode);
			
		} break;
		case NOTIFICATION_APPLICATION_FOCUS_IN: {
			
			OS::get_singleton()->set_low_processor_usage_mode_sleep_usec(int(EDITOR_GET("interface/editor/low_processor_mode_sleep_usec")));
			EditorFileSystem::get_singleton()->scan_changes();
			_scan_external_changes();
			GDExtensionManager *gdextension_manager = GDExtensionManager::get_singleton();
			callable_mp(gdextension_manager, &GDExtensionManager::reload_extensions).call_deferred();
		} break;
		case NOTIFICATION_APPLICATION_FOCUS_OUT: {
			
			if (EDITOR_GET("interface/editor/save_on_focus_loss")) {
				_menu_option_confirm(FILE_SAVE_SCENE, false);
			}
			
			OS::get_singleton()->set_low_processor_usage_mode_sleep_usec(int(EDITOR_GET("interface/editor/unfocused_low_processor_mode_sleep_usec")));
		} break;
		case NOTIFICATION_WM_ABOUT: {
			show_about();
		} break;
		case NOTIFICATION_WM_CLOSE_REQUEST: {
			_menu_option_confirm(FILE_QUIT, false);