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Is there a way to copy an existing docker image from one ecr repo to another using Pulumi?

I'm not aware of a way to copy using Pulumi - it can be done with a self-hosted GitHub/GitLab runner though.
Why do you need it copied? Pulumi can build and store an image that is identical to the one you are speaking of in the newly specified ECR repo.

I’m considering a model where the image is created in CI and pushed to a “build repo.” Then when it comes time to deploy it, it would be copied to the “deploy repo,” followed by other deployment steps like creating a lambda. The deploy steps I want to do in Pulumi.

What you can do with Pulumi is <https://repost.aws/knowledge-center/secondary-account-access-ecr>

Otherwise <https://github.com/containers/skopeo#copying-images|skopeo> can be used to copy an image.