Firstly, it is unclear where your application was deployed? App Engine Standard? Or App Engine flexible? The setup of App Engine Standard and Flex are quite different.
Downloading your Node.js source code from your Google App Engine is not supported at the moment. There is a Feature request[1] submitted for the implementation of the Source code download(For all Supported GCP programming languages) for App Engine, however, this has been considered internally as infeasible at the moment. Only a few requests have been received for this feature to be implemented(you can click the +1 button on the request to add your vote for the implementation). As a matter of fact, the GCP team recommends avoiding the use of App Engine as a source control, which is why this feature is not available. There used to be certain App Engine SDKs[2] that allow this(which information available to me, at the moment, suggests are now deprecated), but certainly not available for node.js.