feat: Migrate kubeflow/kubeflow example_notebook_servers_publish.yaml GitHub Action to kubeflow/notebooks - notebooks-v1 branch

[liavweiss]

Summary
This PR migrates the GitHub Actions workflow responsible for building and publishing all notebook server example images from the kubeflow/kubeflow repository to the kubeflow/notebooks repository.

Related: #614

Verification
Successfully built and published all notebook server example images:
https://github.com/liavweiss?tab=packages&repo_name=notebooks

I kept ghcr.io/kubeflow/kubeflow/notebook-servers as it is, after this comment #585 (comment)

[google-oss-prow]

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[andyatmiami]

/ok-to-test

[andyatmiami]

Thanks for getting this PR opened up and performing validations on your end @liavweiss . Workflow files included are properly customized for kubeflow/notebooks while also preserving the original logic present in kubeflow/kubeflow.

I can happily confirm I am able to replicate this success on my own fork:

• https://github.com/andyatmiami/kubeflow-notebooks/actions/runs/18291001715/workflow

Please note I did add a commit to my fork to ensure I was not publishing packages to kubeflow org

• andyatmiami@05bca9f

With that change - all images were rebuilt on a VERSION change and appear listed under my Packages in GitHub:

• https://github.com/andyatmiami?tab=packages&tab=packages&q=notebook-servers