Is there a way to stop an ec2 instance using the automation API?

Not using the api itself. An automation-api program can call the AWS SDK, which has functions for this.

Thanks tenwit, I ended up using your solution. Although I find the lack of such function strange.

There isn't a Pulumi function to send a HTTP request to an API gateway either... Pulumi is a provisioning tool. It doesn't provide APIs for using the provisioned resources.