Not the OP, but here's my understanding.
> What is the shape of this "not journalism at all" category? How can I distinguish non-journalism from non-objective journalism or journalism on a topic I don't personally think is important?
For the NYTimes, anything from the opinion section, anything the second half of the category list (Arts, Books, Style, Food, Travel, Magazine, etc.) I would consider is held to a lesser standard than the first half (World, U.S., Politics, N.Y., Business). Also, articles in those sections were less likely to be about current events specifically, and might include reviews, interviews, and other content that isn't "of the day". The Opinion section is actually a nice divider.
> Do news organizations offer any explicit disclaimers that their "non-journalism" has low editorial standards and shouldn't be trusted the same way as their journalism? Or is it just something you have to know?
Outside of explicit tagging of Opinion pieces as such, no. In the old days, in paper form, you generally knew that anything in section A was solid journalism, other than the opinion pieces in the back, and in Column 1 of the front page. Section B (Local news), was usually okay, but could get a little weak further to the back. Section C (Sports) was good on game facts, but other stuff could be weak. Section D (Business) was usually good again, but was much more likely to also include PR fluff pieces and other similar stuff. Section E and beyond (Arts/Calendar, Comics, etc.) was all less serious. Parade Magazine, an insert that showed up in many publications across the US was complete garbage.
> * Does the average media-literate person know any of this?
Most people knew about the opinions section, it was pretty clear back then that the paper didn't stand behind those pieces, and they only represented their author's opinion. The feel of each section and the advertisements included therein did give some sense of the importance of the section.
I have felt for some time that the loss of the metadata around opinion pieces has done real damage to Journalism, and that it would be good for publications to come up with some standard for identifying that, to reduce the instances of breathless reports of "The Washington Post is a socialist rag!" after a single opinion piece by an actual socialist is published.