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My use case is this: I have a domain that points to a server at IP 1.2.3.4 and I would like a subdomain at the domain to point to my App Engine application i.e.
example.com --> 1.2.3.4
app.example.com --> App Engine application
The naked domain as well as the www subdomain must point to the standalone server.
From what I've found out so far, this doesn't seem possible.
Would anyone be able to confirm if this configuration is indeed not possible?

Yes, I can confirm this is possible. In fact, it is the recommended way for handling the microservice architecture on App Engine [0].
In your case specifically, all you have to do is create a CNAME with your DNS registrar pointing to ghs.googlehosted.com.
You then have to first verify your TLD with App Engine and add a specific mapping to your subdomain as described here [1].
Let me know if you have any specific questions with the process.
[0] https://cloud.google.com/appengine/docs/standard/python/microservices-on-app-engine
[1] https://cloud.google.com/appengine/docs/standard/python/console/using-custom-domains-and-ssl