Workflow `GITHUB_TOKEN` not authorised to download packages from GitHub registry - github

Question

Following this documentation, I'm using the default GITHUB_TOKEN secret to download & publish packages from another repository of mine (same scope) on GitHub registry, from a workflow. Yarn is configured to use the environment variable GITHUB_TOKEN. When using the default GITHUB_TOKEN secret, I get a 403 (Forbidden) error when downloading the package.
When using a PAT (a secret named TOKEN that I define manually with write:packages right), it works fine, when not using any token, I get a different error. Therefore, I assume the token is well transmitted and there is a right issue.
What am I missing?
Thank you.
Here is my repository settings (Actions > General) :
Allow all actions and reusable workflows: Any action or reusable workflow can be used, regardless of who authored it or where it is defined.
Read & write permissions: Workflows have read and write permissions in the repository for all scopes.
Here is a test workflow (link here):
name: Test Token
on:
workflow_dispatch:
jobs:
# Fail
github:
name: Test GitHub Token
runs-on: ubuntu-latest
steps:
- name: Checkout the repository
uses: actions/checkout#v3
- name: Setup Node
uses: actions/setup-node#v3
with:
node-version: 18
- name: Install dependencies
run: yarn install
env:
GITHUB_TOKEN: ${{ secrets.GITHUB_TOKEN }}
# Success
pat:
name: Test PAT
runs-on: ubuntu-latest
steps:
- name: Checkout the repository
uses: actions/checkout#v3
- name: Setup Node
uses: actions/setup-node#v3
with:
node-version: 18
- name: Install dependencies
run: yarn install
env:
GITHUB_TOKEN: ${{ secrets.TOKEN }}