I believe if you need to use the kubeconfig for something that is not a Pulumi provider (i.e. using the kubeconfig` as an input to create a provider), you’d probably want to use the Automation API, where you would run your stack, have it export the kubeconfig, and then use that exported value in your code once the stack has run.
While Pulumi is running I’m not sure it’s possible to get the concrete value of kubeconfig, since the cluster may not have been created yet, as resource creation is async