### 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
String config_error;
					bool missing_templates;
					if (export_defer.android_build_template) {
						export_template_manager->install_android_template();
					}
					if (!platform->can_export(export_preset, config_error, missing_templates, export_defer.debug)) {
						ERR_PRINT(vformat("Cannot export project with preset \"%s\" due to configuration errors:\n%s", preset_name, config_error));
						err = missing_templates ? ERR_FILE_NOT_FOUND : ERR_UNCONFIGURED;
					} else {
						platform->clear_messages();
						err = platform->export_project(export_preset, export_defer.debug, export_path);
					}
				}
				if (err != OK) {
					export_error = vformat("Project export for preset \"%s\" failed.", preset_name);
				} else if (platform->get_worst_message_type() >= EditorExportPlatform::EXPORT_MESSAGE_WARNING) {
					export_error = vformat("Project export for preset \"%s\" completed with warnings.", preset_name);
				}
			}
		}
		if (err != OK) {
			ERR_PRINT(export_error);
			_exit_editor(EXIT_FAILURE);
		} else if (!export_error.is_empty()) {
			WARN_PRINT(export_error);
		}
		_exit_editor(EXIT_SUCCESS);
	}
}
void EditorNode::_resources_reimported(const Vector<String> &p_resources) {