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I think you are looking for: <https://www.pulumi.com/docs/reference/pkg/nodejs/pulumi/aws/ecs/#>
And the `TaskDefinition` and `Service` resources specifically.
For scheduled tasks, I think you then use cloudwatch (<https://www.pulumi.com/docs/reference/pkg/nodejs/pulumi/aws/cloudwatch/>) `EventRule` and `EventTarget`

Looks like you’re right!  I was misled by the fact that I was setting them up manually in ECS without touching CloudWatch at all.  I didn’t realise that what I was doing in ECS was being translated to CloudWatch behind the scenes.  Thanks for the info!