A stack is another instance of the same set of infrastructure. So that sounds about right.
So in your question, a project ID is a GCP concept, not a Pulumi one? If that's right, then I don't know the answer. This doesn't seems like a question for #C02DM3GH4TY, which is about the Pulumi application web UI and API. You might be better off asking in #CRFUR2DGB