I do not have much experience dealing with Argon2ID. However, the scaling behavior of your App Engine instance depends on how you set it up as well as which environment of App Engine it is running in. Since you mentioned you are running on standard, you will notice that scaling of the application will be rapid. I believe it would be worth to check the following documentation
here out as it pertains to how instances are managed on standard. You will see that you can set a array of attributes to allow the app to scale the way you prefer by either
Manual , Automatic, Basic scaling. As you mentioned that Argon2Id "is both memory and CPU intensive"as well as automatic scaling, you can set certain parameters of automatic scaling such as:
Target CPU Utilization,
Target Throughput Utilization,
Max Concurrent Requests.
Lastly, you may set the configuration file to specify the
scaling type and instance class of the version you deploy on App Engine.
Scaling type controls how instances are created while the
instance class determines the compute resources such as memory size and CPU speed. You may feel free to explore more information about this
here.
I hope I was able to help with the scaling part of your question!