CLI-driven remote run: "error looking up module versions: 401 Unauthorized"

Problem

When running terraform init against a Terraform Enterprise or HCP Terraform Workspace using the remote backend or cloud configuration, receive error:

│ Error: Error accessing remote module registry
│ 
│   on main.tf line 39:
│   39: module "example" {
│ 
│ Failed to retrieve available versions for module "example" (main.tf:39) from app.terraform.io: error looking up module versions: 401 Unauthorized.

Prerequisites

• Local, CLI-driven Terraform execution
• Module located in Private Module Registry

Cause

• Missing valid CLI Configuration File with credentials or credentials created by terraform login 

Solution

• Provide a valid credential token to Terraform Enterprise or HCP Terraform either using terraform login or by creating a CLI Configuration File with credentials

Note: it is not sufficient to supply a token argument in the cloud or remote backend configuration to be able to read private module registry modules

Outcome

The terraform init command succeeds without error

Additional Information

• https://developer.hashicorp.com/terraform/cli/config/config-file#credentials-1

• Module Registry shows this requirement: