fix(docfx): remove redundant standalone cleanup step

[Chris-Wolfgang]

Summary

Mirrors repo-template#342. Removes the standalone "Clean up stale root files from gh-pages" step in docfx.yaml because the deploy step already does identical cleanup in its own worktree.

Why

On every release with deploy_as_latest=true, gh-pages was receiving two commits + two Pages rebuilds:

1. chore: clean up stale root DocFX assets before redeploy [skip ci] (standalone cleanup)
2. docs: deploy <version> and update latest (deploy step — also re-cleaned in its fresh worktree)

The deploy step already does the exact same Get-ChildItem | Where-Object | Remove-Item cleanup at lines 360-363 of docfx.yaml (well, those line numbers were before this PR — the cleanup is now closer to the top of the deploy step). The standalone step's cleanup commit was redundant duplication, and its only meaningful behavior was to expose a partial-cleanup window — if the deploy failed after the standalone step pushed, gh-pages was stuck in cleaned-but-no-fresh-content state.

Impact

• ✅ One commit + push per release (atomic deploy)
• ✅ Half the pages-build-deployment rebuilds
• ✅ Eliminates the partial-cleanup window
• ✅ ~60 fewer lines of YAML

Why now

Caught by Copilot review on PR #95 (lines 234, 282 — both call sites of the cleanup-push). Fix lands locally rather than waiting for a template-sync wave so IEnumerable doesn't carry the redundancy between now and then.

Note about the protected-files guard

Touches .github/workflows/docfx.yaml so the Detect .NET Projects guard will fail it. Maintainer override required.

Test plan

• Maintainer override + merge
• Either order with repo-template#342 is fine; both end up with the same fix
• Verify on next release that gh-pages receives one commit per deploy

[Copilot]

Pull request overview

Removes a redundant gh-pages “stale root cleanup” step from the DocFX deployment workflow, relying on the existing cleanup that already occurs inside the single-commit deploy step to avoid double commits / double Pages rebuilds and reduce the risk of a partial-cleanup state.

Changes:

• Deleted the standalone “Clean up stale root files from gh-pages” step.
• Kept root cleanup behavior consolidated within the “Deploy docs to GitHub Pages” step (single worktree/repo state, single push).

[Copilot]

Pull request overview

Copilot reviewed 1 out of 1 changed files in this pull request and generated no new comments.

[Chris-Wolfgang]

Superseded by the C1 template-drift re-sync. The canonical repo-template docfx.yaml no longer contains the redundant 'Clean up stale root files from gh-pages' step (removed upstream). PR #135 re-syncs docfx.yaml from canonical, delivering this removal. Closing as superseded; deleting the branch.