Is your feature request related to a problem? Please describe.

Whenever we try to push the image to production using make push we get an authentication error.

Describe the solution you'd like

Add cloudbuild.yaml that will run the Makefile, to build the image with the details of the project it is in (so us-docker.pkg.dev/${PROJECT_ID}/examples) so it pushes the image to that project's repository.
Describe alternatives you've considered

Leave this alone, and keep it as is. But gives a consistent experience for managing and pushing images.

Additional context
NA
Examples checklist

• simple-genai-server