CI workflow triggered but not shown in checks for PRs marked as ready for review

This concerns my newly implemented feature to [skip the ci.yml workflow for draft PRs](https://github.com/galaxyproject/training-material/pull/3963).

When you turn such a PR into a ready-for-review one, the expectation was that this very event should trigger the workflow and a build-site job should run.

This is indeed what's happening, however, that build-site run is only showing up in the "Checks" tab, but the status checks section in the Conversations tab does not get updated so there is no direct visual cue for the PR author or the reviewers to see that a test was run and what it's result was.

Not sure whether this is an unavoidable github UI issue, or whether this can be addressed somehow in the workflow definition, or in the required status checks section of the settings.