deploy-pages: incompatible with GitHub Pages artifact-based deployment

[sam-caldwell]

Bug

The deploy-pages action expects a publish_dir input (defaulting to public) and appears to deploy by pushing files to a branch. However, the standard GitHub Pages deployment flow uses:

1. upload-pages-artifact — creates and uploads a tar.gz artifact
2. deploy-pages — downloads that artifact and deploys via the Pages API with OIDC authentication

The internal deploy-pages action fails with:

publish_dir does not exist: public

Because the workflow doesn't have a local public directory — the site was packaged as an artifact in the previous job.

Expected Behavior

The action should:

1. Download the github-pages artifact from the current workflow
2. Deploy it via the GitHub Pages deployment API (POST /repos/{owner}/{repo}/pages/deployments)
3. Use OIDC token exchange for authentication (requires id-token: write)
4. Output page_url

Current Workflow Pattern

build-website:
  steps:
    - uses: asymmetric-effort/actions/actions/upload-pages-artifact@...
      with:
        path: website/dist

deploy-website:
  needs: build-website
  permissions:
    pages: write
    id-token: write
  steps:
    - uses: asymmetric-effort/actions/actions/deploy-pages@...
      # No inputs needed — it should find the artifact automatically