Is this the screenshot of the endpoint deployed with sagemaker-sdk or with terraform?
Beware that when you set HF_MODEL_ID and provide a model_data the model_data is ignored.

Not certain I understand what you mean by providing the env for HF_TASK . Do you mean you think I should add a new env variable under my “huggingface” model in the tf?

You need do add HF_TASK as environment in the terraform aws_sagemaker_model  https://registry.terraform.io/providers/hashicorp/aws/latest/docs/resources/sagemaker_model#environment 1