docfx: sync from repo-template (gh-pages bootstrap fix)

[Chris-Wolfgang]

Summary

Sync .github/workflows/docfx.yaml from repo-template to pick up the gh-pages bootstrap fix from Chris-Wolfgang/repo-template#337.

What changed

The "Deploy docs to GitHub Pages" step had a latent bug: when the gh-pages branch did not yet exist on the remote, $WORK_DIR was created as a plain directory and the subsequent git add / diff --cached / commit / push failed with fatal: not a git repository. The fix initializes the directory as a git repo on gh-pages and adds the authenticated origin remote, so the existing add/commit/push works on a first-ever deploy. Cleanup also branches between git worktree remove (worktree path) and Remove-Item (fresh-repo path).

If gh-pages already exists in this repo (the common case), this change is a no-op at runtime — the bootstrap branch is only taken on a fresh repo.

Test plan

• Workflow YAML lints / next docs deploy succeeds
• (Optional) verify gh-pages is unaffected

[Copilot]

Pull request overview

Note

Copilot was unable to run its full agentic suite in this review.

Syncs the DocFX GitHub Pages deployment workflow with the repo-template fix so first-time deployments succeed when gh-pages doesn’t exist remotely.

Changes:

• Detect whether gh-pages exists and branch between worktree vs. fresh repo bootstrap.
• Initialize a real git repo in $WORK_DIR (with origin) when bootstrapping gh-pages.
• Adjust cleanup to remove a worktree vs. deleting the fresh directory, and reset $LASTEXITCODE.

[Chris-Wolfgang]

Superseded — the gh-pages bootstrap fix is in canonical-protected (now folded into the vNext → main PR for the per-repo release pilot).