chore(ci): auto-sync Docker Hub images to ghcr.io and switch tests to use them

Some of the tests currently pull public images from Docker Hub, which can intermittently hit rate limits and cause workflow failures unrelated to any code changes. To make the test runs more reliable, it would help to mirror the images we use and have the tests pull from those mirrors instead.

Proposed Approach

1. Add a scheduled GitHub Actions workflow

   • Pull the images used by our tests (e.g., alpine, hello-world, etc.) from Docker Hub
   • Push them to our existing location on ghcr.io using the same tags
     This keeps our mirrored copies updated without manual work.

2. Update the tests
   Switch the image references to the mirrored versions on ghcr.io so they no longer depend on Docker Hub.

If this approach sounds good, I’m happy to open an initial PR that adds the sync workflow and updates the test image references.

Start by locating the existing GitHub Actions workflows and the tests that pull public images such as alpine and hello-world. Review how the repository publishes images to ghcr.io, then update the scheduled sync workflow and test image references. Done means the mirrored tags are refreshed automatically and tests no longer pull these images from Docker Hub.