Use AWS Trusted Advisor to obtain a report containing the checked items in the Cost Optimization pillar

Download the detailed billing report, upload it to a database, and match the line items with a list of known resources by department.

Create a script by using the AWS CLI to automatically apply tags to existing resources (or each department. Schedule the script to run weekly.

Use AWS Organizations to create a department Organizational Unit and allow only authorized personnel in each department to create resources.

Create a Budget from the Billing and Cost Management console. Specify the budget type as Cost, assign tags for each department, define notifications, and specify any other options as required.