AWS RDS Aurora Serverless instances are listed under 'RDS - Other' in the AWS Cost History Report.
Filtering a FlexReport can help isolate Aurora Serverless instance details. An example for a monthly aggregate is shown in the screenshot below:
Serverless instances are not supported within asset reports and perspectives.
There may be rare situations where as subset of serverless instances will appear in asset reports and be visible in perspectives. This is due to the instance historically being a supported instance type and then converted to serverless at a future point in time.