Any way to checkout PR from `issue_comment` event?

The example in the docs here assumes a pull request event, but it does not work when operating on Pull Request comments, since those come through the issue_comment event.

I've spent several hours on this now and I don't see any way to checkout the branch associated with the issue_event.

Complications:

• The event is the comment and it links to an issue, which only indirectly seems to have data on the pull request url.
• Checking out the associate sha doesn't give push ability, since the branch name itself is not discoverable (at least not as well as I can tell).
• Since issue_comment events have to be triggered by the workflow file on the default branch, it seems that is always the branch name provided. I haven't yet found any way to get the actual PR branch, although it seems this should be a straightforward and frequent use case for operating on PR comments.

Start by reading the linked checkout pull-request documentation and the issue_comment event details described here. Determine whether the action can identify the pull request's head branch and provide push-capable checkout behavior for comments; done means a documented, reliable workflow or a clearly scoped action change.