What is the workaround for errors like this?

sdk-v2/provider2.go:385: sdk.helper_schema: Error creating App: POST <https://api.digitalocean.com/v2/apps>: 409 (request "8e8115a8-16cf-49e8-8c13-e14d6d5b011a") App name already exists: provider=digitalocean@4.31.1

I'd like to complete deployment of my stack.

Based on the error it appears you need to change the name of your app or if you want to reuse existing infra you'd need to import it into Pulumi via

pulumi import ...

The importing may work, however this is counter intuitive as a worflow. The resources before it exists but no app/resource exist error. I suspect the reason why there is an error on this resource seems to be a derivative of the fact that it had an error before on its creation, and so was never "fully" created. Thus it should make sense that the second time around pulumi should either sync as fully created or restate the original error.

That depends on whether or not the pulumi update got to the point of receiving enough information back from the provider to know whether something exists or not. Eg- if Pulumi tells provider A to create a resource and the update is interrupted before Pulumi gets confirmation that something is actually created, then there really isn't a way for Pulumi to sync.