`check_style.sh` fails to post comments in external PRs

Our `check_style.sh` script is supposed to post the errors it finds as a comment in the PR. E.g. https://github.com/ethereum/solidity/pull/10653#issuecomment-748128097. Looks like it does not work with external PRs, due to permission issues. For example in [1184923](https://app.circleci.com/pipelines/github/ethereum/solidity/26748/workflows/45c1a6ca-bb58-40fe-ad72-4cc8681d1cf3/jobs/1184923) from #13595 you can see this error:
```
posting error message to github
{
"message": "Requires authentication",
"documentation_url": "https://docs.github.com/rest/reference/issues#create-an-issue-comment"
}
ERROR: Error message does not contain file path.
```
and there's no comment in the issue.

Is there something we can do to fix it? The bug tracker is public so CI should not need any specific permissions/tokens to post a comment, even when it's someone not from the team triggering it.

Fixing this save us having to constantly point this out in external PR reviews.

Start by inspecting check_style.sh and the CircleCI job linked in the issue, then trace its request to GitHub's issue-comment API for external pull requests. Done means style errors are posted as comments on external PRs without the current authentication failure, while the existing file-path error behavior remains visible.

Written by the indexing model from the issue text.