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It's possible the Console is doing some work for you that you will need to explicitly define in your Pulumi app.

When trying to replicate a solution from AWS I typically look for the related AWS documentation that shows how to achieve something via the API and that's easier to replicate to Pulumi. If you can share the AWS doc link that describes what you're doing, I can try to point you in the right direction in Pulumi's docs.

<https://docs.aws.amazon.com/secretsmanager/latest/userguide/tutorials_db-rotate.html|https://docs.aws.amazon.com/secretsmanager/latest/userguide/tutorials_db-rotate.html>

Looking at that I suspect the console is doing what's described at <https://docs.aws.amazon.com/secretsmanager/latest/userguide/enable-rotation-rds.html> on your behalf. The "Creating a Lambda rotation function using an AWS Serverless Application Repository template" section on that page describes a Cloudformation stack that does the same thing which could be replicated in Pulumi.