Deploy to another repository

I manage the time-rs organization, which has a website located at https://time-rs.github.io. The source for this is generated from two separate repositories: time-rs/time and time-rs/book. I would like to have a shared workflow that deploys to time-rs/time-rs.github.io, such that I can have a landing page (as is currently the case).

My attempt at doing this was to create a workflow to build everything from scratch, which works as expected. However, when trying to use it as a reusable workflow, it failed because it is trying to deploy it to the caller's GitHub pages. This is not what I want.

Would it be possible to add the ability to deploy the pages to another repository? I presume this would need a PAT, but that is acceptable to me. The alternative is using the branch-based method that I have been using for years, even if it is less than ideal.

Start by reviewing the reusable workflow behavior described in the issue and how the deployment target is currently determined. Done means a workflow can deploy GitHub Pages artifacts to a separately specified repository, with the required PAT-based authentication documented and verified.