All pulumi examples configure k8s provider with:

cmd-args: config config-helper --format=json
        cmd-path: gcloud
        expiry-key: '{.credential.token_expiry}'
        token-key: '{.credential.access_token}'

which I think totally ignores

{ provider: ... }

argument used to create

gcp.container.Cluster

, and just picks whatever env vars or ~/.config/gcloud points to