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Is it a case of <https://github.com/pulumi/pulumi-gcp/issues/129> ?

Yes - and unfortunately the upstream Google Terraform provider folks explicitly decided they did not want to improve this:

<https://github.com/terraform-providers/terraform-provider-google/issues/4071#issuecomment-514291169>

yeah, but knowing it Pulumi can choose to always explicitly pass project in options, this way you can default to whatever google SDK defaults to  and catch errors this way, before even calling TF