Expend automation to be event driven

#5 and #4 could be extended to be called upon release of upstream tooling to publish the docs site. This could be done with repository_dispatch events (which have their own limitations) or by a webhook to an external listener to kick this off elsewhere.

Start by reading issues #4 and #5 to understand the existing documentation publishing automation. Compare repository_dispatch with a webhook and external listener, then define the event flow and confirm that an upstream release reliably publishes the docs site.

Written by the indexing model from the issue text.