If you not set any extra labels with runner_extra_labels, because the default ones "self-hosted,${var.runner_os},${var.runner_architecture} would be good enough, you cannot use runner_enable_workflow_job_labels_check as this prevent scaling of any runners:

 Received workflow job event with labels: '["self-hosted","linux","arm64"]'. The event does NOT match the runner labels: 'self-hosted,linux,x64,'

A dummy label in runner_extra_labels would be a workaround but then one must update any runs-on: [self-hosted, linux, x64] to runs-on: [self-hosted, linux, x64, dummy] as long as https://github.com/philips-labs/terraform-aws-github-runner/issues/1714 is unsolved.

Maybe runner_labels could be a added as variable of the main module with "self-hosted,${var.runner_os},${var.runner_architecture} as default value. So it can be overridden completely of needed. Then runner_extra_labels is not needed anymore.