docfx: bootstrap gh-pages branch on first deploy

[Chris-Wolfgang]

Summary

• The "Deploy docs to GitHub Pages" step had a latent bug: when gh-pages did not yet exist on the remote, $WORK_DIR was created as a plain directory and the subsequent git add / diff --cached / commit / push calls all failed with fatal: not a git repository (and error: unknown option 'cached').
• Fix: after creating the empty $WORK_DIR, initialize it as a git repo on the gh-pages branch and add the authenticated origin remote, so the existing add/commit/push flow works on the first-ever deploy.

Reproduction

Hit in IComparable-Extensions, run 25606117292. Workaround was to manually create an orphan gh-pages branch with .nojekyll and re-run.

Downstream impact

This is repo-template — once merged, the change should propagate to all downstream repos via the standard pr.yaml / docfx.yaml template sync. Reviewers and downstream maintainers should expect to see this as part of the next sync PR in each consuming repo.

Test plan

• Merge and let the next downstream sync pick it up
• Verify on a repo with no gh-pages branch that the first docs deploy succeeds end-to-end (init → add → commit → push)
• Confirm existing repos (with gh-pages already present) are unaffected — the change only runs in the else branch

[Copilot]

Pull request overview

This PR updates the DocFX GitHub Actions workflow to support the first-ever docs deployment in repositories that do not yet have a gh-pages branch, by creating a valid git repository in the temporary deploy directory so the existing add/commit/push sequence can run successfully.

Changes:

• When gh-pages is missing, create $WORK_DIR and initialize it as a git repo on gh-pages.
• Add an authenticated origin remote in $WORK_DIR so the later push works in the bootstrap case.