AWS Batch: how to propagate tags to ECS clusters and EC2 auto scaling groups?

When setting up a managed compute environment, AWS Batch allows to set tags on compute resources it creates. Per my experiments these tags get only applied to EC2 instances launched in the compute environment, but not to the ECS cluster nor the EC2 auto scaling group created for the environment.

Is this a bug in AWS Batch? If not, what's the recommended way to propagate tags to Batch-initiated ECS clusters and auto scaling groups?