This JavaScript GitHub Action can be used to impersonate a GitHub App when secrets.GITHUB_TOKEN's limitations are too restrictive and a personal access token is not suitable.

For instance, from GitHub Actions' docs:

When you use the repository's GITHUB_TOKEN to perform tasks, events triggered by the GITHUB_TOKEN, with the exception of workflow_dispatch and repository_dispatch, will not create a new workflow run. This prevents you from accidentally creating recursive workflow runs. For example, if a workflow run pushes code using the repository's GITHUB_TOKEN, a new workflow will not run even when the repository contains a workflow configured to run when push events occur.

A workaround is to use a personal access token from a personal user/bot account. However, for organizations, GitHub Apps are a more appropriate automation solution.

jobs:
 job:
 runs-on: ubuntu-latest
 steps:
 - name: Generate token
 id: generate_token
 uses: tibdex/github-app-token@v1
 with:
 app_id: ${{ secrets.APP_ID }}
 # Optional.
 # github_api_url: https://api.example.com
 # Optional.
 # installation_id: 1337
 # Optional.
 # Using a YAML multiline string to avoid escaping the JSON quotes.
 # permissions: >-
 # {"members": "read"}
 private_key: ${{ secrets.PRIVATE_KEY }}
 # Optional.
 # repository: owner/repo
 - name: Use token
 env:
 TOKEN: ${{ steps.generate_token.outputs.token }}
 run: |
 echo "The generated token is masked: ${TOKEN}"

Another use case for this action can (or could) be found in GitHub's own docs.