Bug located in how the Changelog Action interacts with GitHub Environments

### 🔍 Before submitting the issue

- [x] I have searched among the existing issues
- [x] I am using a Python virtual environment

### 🐞 Description of the bug

Our setup for publishing with the trusted publisher workflow leverages environments to secure access to publishing new versions of packages. The intended workflow for environments with approvals is that the person triggering the workflow is not able to approve their own request.

The doc deploy changelog workflow circumvents this security by triggering a follow up workflow run as the pyansys bot, this means a user is then able to approve their own publish. This may be acceptable or it may not, but ideally the follow up run would be triggered as the same user who initially pushed the tag.

### 📝 Steps to reproduce

Publish a tag on a repository that has trusted publisher enabled with an environment

### 💻 Which operating system are you using?

Windows

### 📀 Which ANSYS version are you using?

_No response_

### 🐍 Which Python version are you using?

3.9

### 📦 Installed packages

n/a

Start by tracing the doc deploy changelog workflow and its follow-up run in the repository's GitHub Actions configuration, then compare it with the trusted publisher workflow and GitHub Environment approval behavior. Done means a tag-triggered publish retains the original user's identity so that user cannot approve their own publishing request.

Written by the indexing model from the issue text.