[CI] [GHA] Use another token to create PR for the auto-generated Python stubs (#32077)
### Details:
As per https://github.com/orgs/community/discussions/57484 &
https://github.com/orgs/community/discussions/65321
PRs created with the default `GITHUB_TOKEN` would not have workflows
triggered. The docs read:
```
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.
```
in
[link](https://docs.github.com/en/actions/concepts/security/github_token#when-github_token-triggers-workflow-runs).
If we use a generated PAT, the workflows should be triggered.
### Tickets:
- *173561*