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

Updates the DocFX GitHub Actions workflow to correctly bootstrap a first-time gh-pages deployment by initializing a fresh git repo when the remote gh-pages branch does not yet exist, while preserving the existing worktree-based flow when it does.

Changes:

• Detect whether gh-pages exists and branch between a worktree-based deploy vs. fresh repo initialization.
• When gh-pages is missing, initialize $WORK_DIR as a git repo on gh-pages and add an authenticated origin remote so later add/commit/push works.
• Adjust cleanup to remove either the worktree or the fresh directory.

[Chris-Wolfgang]

Superseded by PR #101 (D8 canonical refresh). The wholesale canonical sync of docfx.yaml from repo-template includes the gh-pages bootstrap fix this PR was targeting, plus the inline root-redirect refactor that landed canonical after this PR was opened.

Closing as no-longer-needed. Branch fix/docfx-bootstrap-gh-pages can be deleted.