Oh geeez… I’m not sure you want me doing that.
As with all things, there is the actual and the mental model (including physics). Some refer to actual history, which can never be exactly known and some refer to “history” as being merely whatever is currently documented (and often erased and rewritten). The mind identifies or objectizes (forms a mental picture or as a mental object) situations or events and records them as historical events based on relevance.
Those who record history for sake of humanity, identify some things as relevant and others as irrelevant and document the relevant ones. New ages bring people who then erase or alter documents so as to further their chosen cause.
So the idea of no one ever documenting anything seen as relevant means that the age that has been entered regards no changes as relevant and thus either doesn’t document them or merely documents them as an ambiguous repeated cycle. Or perhaps, as suggested, we simply stop calling it “our history” because there are no more humans to consider anything relevant.
As long as some living entity exists, there will always be a personal history relevant to that individual, at least. And it is hard for me to imagine even the possibility of life continuing in any form without any recording of social events marked as significant moments of change as far as those lives are concerned. Every small town and family has its historical events.
So the only thing that I could safely call the “historical essentials” that are being referred to would be the globally public announcements concerning globally significant events standing out above the average enough to be note worthy.
The greater issue is of course, the contrived historical announcing, a purely imaginary history for sake of an artificially propagated society being told of events so as to inspire them in certain ways even though those events never really occurred (The Matrix scenario). The more people believe what they are told via a news mediator, the more invention of history occurs and the less anyone knows of it being completely fake.
So to a public, history could never actually end because either the level of relevance will shift so as to make formerly irrelevant things noteworthy or invented historical scenarios will be told to them regardless of perhaps nothing actually relevant changing.