As a moderator, one of the 'powers' I have is to create and feature a chat event, which is something I distinctly remember using to 'advertise' a sitewide cleanup years ago.
While an RO can create events for their room, as I understand it, the moderator dialog is a little different.
On Super User, the page says:
On the equivalent page on MSE, the page says:
Now, as a moderator on Meta Stack Exchange and not a site without a name, I'm curious to whether an event I create would be advertised on MSE, not at all, or if Meta has a special scope?