[Bug]: Regression on latest version, potentially related to PR #751 #770

Pre-flight checks

• I searched existing issues and did not find a duplicate
• I reproduced this with the latest released version or current master
• I included a reproducible example or a sanitized/redacted reproduction path if the original repository is private

action-gh-release version

latest

Runner operating system

ubuntu-latest

Release target repository

No response

Reproduction repo, gist, or artifact

No response

Workflow snippet

- name: Create GitHub release
      uses: softprops/action-gh-release@v2
      with:
        tag_name: ${{ steps.bump.outputs.new_tag }}
        name: Release ${{ steps.bump.outputs.new_tag }}
        body: ${{ inputs.release-message }}
        generate_release_notes: true
        append_body: true
      env:
        GITHUB_TOKEN: ${{ inputs.github-token }}

Expected behavior

Before this release, when using the action, I was able to run more workflows after this one was executed.

on:
  release: 
    types: [published]
``

### Actual behavior

on:
release:
types: [published]
``
Is not being triggered because of the token, so I updated the workflow to use:

- name: Create GitHub release
      uses: softprops/action-gh-release@v2
      with:
        tag_name: ${{ steps.bump.outputs.new_tag }}
        name: Release ${{ steps.bump.outputs.new_tag }}
        body: ${{ inputs.release-message }}
        generate_release_notes: true
        append_body: true
        token: ${{ inputs.github-token }}

Steps to reproduce

1. Trigger workflow with env
2. The next workflows does not start because of the token and despite of creating the release.

Relevant logs

Run softprops/action-gh-release@v2
  with:
    tag_name: v1.80.0
    name: Release v1.80.0
    generate_release_notes: true
    append_body: true
    overwrite_files: true
    token: ***
  env:
    GITHUB_TOKEN: ***

Additional context

Please update the documentation to inform users to move to this approach (token) or revert that change that broke pipelines.
Despite of showing token: *** this did not work.
I can improve the docuementation if you are ok with it.