Automatically stop and start an Amazon RDS DB instance in a CDK app

Based on that document, the scheduling is done by System Manager Maintenance Window, There is CDK for that service although it is in L1 Construct (ie. uses the basic Cloudformation structure). Here is the CDK reference: https://docs.aws.amazon.com/cdk/api/v2/docs/aws-cdk-lib.aws_ssm.CfnMaintenanceWindow.html

Alternatively, you can run EventBridge + Lambda to do custom scheduling: https://docs.aws.amazon.com/AmazonCloudWatch/latest/events/RunLambdaSchedule.html.