Resource groups
Resource groups are an organizing feature that bundles many resources (such as EC2 and S3) by a condition like 'belonging to the same project' so you can list and operate on them together in the console.
They are merely a feature to make the management screen easier to view and operate, NOT a mechanism that breaks down the bill amount by department, so it is incorrect. To classify costs in billing, you must activate the tags attached to resources as cost allocation tags.