Publish to AWS: I could not deploy to an existing cloud app

In Publish to AWS, the Existing Targets list did not show my project. I expected to see it there.

Toolkit: 1.89.0.0
Visual Studio: 18.8.2

Start in the Publish to AWS flow, especially how the Existing Targets list is populated, using Toolkit 1.89.0.0 with Visual Studio 18.8.2. Reproduce the missing-project case and compare it with an existing cloud app that does appear; done when the project is listed or the cause is documented and covered by a regression test.

Written by the indexing model from the issue text.