Thanks for the topic (and its related blog article), I missed the two.
However, I had implemented a similar process than the one in the blog, which sends via messaging the data to the extension scope which uses the console.*() methods, taking benefit from only one console to see all the process logs.
But, after our discussion in topic "appAPI.message sync in Firefox and async in Chrome ?", I asked myself about the reliability of the order in which logs are displayed. This is why I was interested in the way the console works in all scopes.
Finally I think the order will be preserved (messaging working probably as a "queue").
One thing to know is : when a console.log data is "output" in console (via messaging + extension scope), the process has probably already kept on working (and if an external event writes in console, this one can be display in console before the extension scope does it with the received messaging data).
That's all for me ! Thanks for links.