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I’m not seeing any issues in the underlying terraform provider: <https://github.com/DataDog/terraform-provider-datadog/issues>

You could always take a stab at creating a dynamic provider as a stopgap.
That’s what I did for API keys before they were supported.

Given the Pulumi provider is a wrapped Terraform provider, the best long term solution is to contribute to the upstream Terraform provider and then ask to update the Pulumi wrapper.
<https://github.com/pulumi/pulumi-datadog/blob/master/provider/go.mod#L17>
This is what we (actually one of my team members) are currently doing for the Keycloak provider.