support: Pushing to external repo fails

[younes-io]

Checklist

• [X] I am using the latest version of this action.
• [X] I have read the latest README and followed the instructions.
• [X] I have read the latest GitHub Actions official documentation and learned the basic spec and concepts.

Describe your question

I have this in a private repository, and I'm trying to use this action to push/publish my Quarto blog to a public repository, blog_p (folder docs contains the HTML/JS/CSS of the website to be served). So, I have created a personal token PAT, as you can see below, which has almost all rights. Yet, this fails

on:
  workflow_dispatch:
  push:
    branches: master

name: Quarto Publish

jobs:
  build-deploy:
    runs-on: ubuntu-latest
    permissions:
      contents: write
    steps:
      - name: Check out repository
        uses: actions/checkout@v4

      - name: Set up Quarto
        uses: quarto-dev/quarto-actions/setup@v2
        with:
          version: 1.4.540

      # Uncomment below to set up R if needed in future
      # - name: Set up R
      #   uses: r-lib/actions/setup-r@v2
      #   with:
      #     r-version: '4.3.2'  # Specify the R version

      # Uncomment below to install R packages if needed in future
      # - name: Install R packages
      #   run: |
      #     Rscript -e "install.packages(c('rmarkdown', 'readr', 'here', 'dplyr', 'tibble', 'purrr', 'stringr'))"

      - name: Install Python and Dependencies
        uses: actions/setup-python@v4
        with:
          python-version: '3.10'
          cache: 'pip'
      - name: Set up Python virtual environment
        run: |
          python -m venv env
          source env/bin/activate
      - run: pip install jupyter
      - name: Install dependencies
        run: |
          pip install -r requirements.txt

      - name: Copy CNAME to root of gh-pages branch
        run: echo "domainname.com" > CNAME

      - name: Render and Publish
        uses: quarto-dev/quarto-actions/publish@v2
        with:
          version: 1.4.540
          target: gh-pages
        env:
          GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
      - name: Debug token
        run: echo "${{ secrets.PAT }}" | sed 's/./& /g' | uniq -c
      - name: Deploy
        uses: peaceiris/actions-gh-pages@v3
        with:
          personal_token: ${{ secrets.PAT }}
          external_repository: younes-io/blog_p
          publish_branch: gh-pages  # default: gh-pages
          publish_dir: ./docs
`` 

### Relevant links

```markdown
Public repository: https://github.com/younes-io/blog_p
YAML config: above
YAML workflow: publish.yaml (above)

Relevant log output

0s
Run echo "" | sed 's/./& /g' | uniq -c
  echo "" | sed 's/./& /g' | uniq -c
  shell: /usr/bin/bash -e {0}
  env:
    BUNDLE_EXT: linux-amd64.deb
    pythonLocation: /opt/hostedtoolcache/Python/3.[1](https://github.com/younes-io/blog/actions/runs/7603837919/job/20706049213#step:10:1)0.13/x64
    PKG_CONFIG_PATH: /opt/hostedtoolcache/Python/3.10.13/x64/lib/pkgconfig
    Python_ROOT_DIR: /opt/hostedtoolcache/Python/3.10.13/x64
    Python[2](https://github.com/younes-io/blog/actions/runs/7603837919/job/20706049213#step:10:2)_ROOT_DIR: /opt/hostedtoolcache/Python/[3](https://github.com/younes-io/blog/actions/runs/7603837919/job/20706049213#step:10:3).10.13/x6[4](https://github.com/younes-io/blog/actions/runs/7603837919/job/20706049213#step:10:4)
    Python3_ROOT_DIR: /opt/hostedtoolcache/Python/3.10.13/x[6](https://github.com/younes-io/blog/actions/runs/7603837919/job/20706049213#step:10:6)4
    LD_LIBRARY_PATH: /opt/hostedtoolcache/Python/3.[10](https://github.com/younes-io/blog/actions/runs/7603837919/job/20706049213#step:10:10).13/x64/lib
      1 
0s
Run peaceiris/actions-gh-pages@v3
[INFO] Usage https://github.com/peaceiris/actions-gh-pages#readme
Dump inputs
Setup auth token
  Error: Action failed with "not found deploy key or tokens"

Additional context.

No response