[codex] Switch image publishing to GHCR

[gankoji]

Summary

Switch the Docker image workflow from Docker Hub to GitHub Container Registry.

What changed

• add the package write permission required for GHCR publishing
• log in to ghcr.io with the built-in GITHUB_TOKEN
• tag published images as ghcr.io/sprocketbot/elo-service:<branch>
• stop pushing images on pull request runs while still building the image
• replace deprecated set-output usage with $GITHUB_OUTPUT

Validation

• parsed .github/workflows/docker-image.yml with Ruby YAML