It's not a zeitgeist, it's a common English sentence structure.
The em-dash observation makes sense. Obviously a minority of people reach for an actual em-dash. The "it's not X, it's Y" complaint is totally bonkers. We might as well call proper spelling a "sign of AI". I.e. yes, AI does it more than humans, but not by so much that it makes sense to be suspicious when you see it.
No one actually used that as a red flag except the OP themselves facetiously so that’s a bad example.
The AI version of what they wrote would be more like: