Sync a wiki with a folder in a repository

wiki.yml

name: wiki
on:
  push:
    branches:
      - main
    paths:
      - wiki/**
      - .github/workflows/wiki.yml
concurrency:
  group: wiki
  cancel-in-progress: true
permissions:
  contents: write
jobs:
  update:
    runs-on: ubuntu-latest
    steps:
      - name: Checkout
        uses: actions/checkout@v3
      - name: Push to wiki
        env:
          GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
        run: |-
          gh auth setup-git
          git config --global user.name 'github-actions[bot]'
          git config --global user.email 'github-actions[bot]@users.noreply.github.com'
          cd wiki
          git init
          git add -A
          git commit --allow-empty-message -m ''
          git remote add origin "${{ github.server_url }}/${{ github.repository }}.wiki.git"
          WIKI_BRANCH="$(git remote show origin | grep "HEAD branch" | sed 's/.*: //')"
          git branch -M $WIKI_BRANCH
          git push -f -u origin $WIKI_BRANCH