Checking out and combining two branches on gh-pages

I did write the following github action:

jobs:
  publish:
    name: Publish
    runs-on: ubuntu-latest
    steps:
      - name: Checkout
        uses: actions/checkout@master
        with:
          ref: develop

      - name: Checkout blog
        uses: actions/checkout@master
        with:
          ref: blog
          path: ./public/blog

      - name: Install SSH Client 🔑
        uses: webfactory/ssh-agent@v0.2.0
        with:
          ssh-private-key: ${{ secrets.ACTIONS_DEPLOY_KEY }}

      - name: Deploy
        uses: JamesIves/github-pages-deploy-action@releases/v3
        with:
          SSH: true
          BRANCH: gh-pages
          FOLDER: public

The public folder is created by the first checkout.
Despite not having an error, the final result is not correct for the blog folder as it is a symlink. Is there anything I am doing wrongly with the way I did nest the checkout of my second (blog) branch ?

Start with the workflow shown in the issue and reproduce the two actions/checkout steps, including the nested ./public/blog path and the gh-pages deployment. Inspect the resulting public/blog entry and determine why it is a symlink; done means the deployed blog folder contains the expected checked-out content.