Currently to copy image from one registry to another without rebuild, build-push-action relies on docker buildx imagetools management command.
Ref: https://docs.docker.com/build/ci/github-actions/copy-image-registries/ and docker/build-push-action#762
If actions-toolkit has the necessary support for imagetools, then another action can be created which imports action-toolkit to do the copy functionality as explained in docker/build-push-action#762