Is there a way to “request” update of MDN?
Yes! Visit the page in question: runtime.onMessage - Mozilla | MDN , hover over “Feedback” at the top and choose “Report a content problem” which will put you in the issue tracker we use for MDN content.
I agree it would be good to document this. Especially for something like the order they fire, I imagine this might be considered an implementation detail and not a thing you should rely on.