While it's true that early historians didn't have the same understanding of history as an academic discipline and consequently didn't use the same methodology as modern day historians, that doesn't mean that they weren't motivated by the same desire to reconstruct past events. You can't read Herodotos or Plinius and not see a resemblance to more recent historical works. Still, historiography obviously underwent enormous changes throughout the years. Like with everything in history, it's more of an evolution than a revolution, but there are a few distinct markers we use within historiography. However, it's important to note that historiography is very much tied to the evolution of human thinking patterns. That's why the historiography in early medieval Europe can't be understood seperately from christianity, just like Leopold Ranke his historism can't be seperated from the effects of the Enlightenment.

So generally these distinct markers within historiography fall in line with the more widely recognized changes within philosophical and intellectual history. The works of ancient Greek historians very much reflects the culture they were a part of, as is true for modern historical works. So to answer your question, what you experience to be a more relatable and academic version of historical writing is widely accepted to have started with Leopold Ranke around the end of the nineteenth century and is closely tied to more widely known terms such as "The Age of Enlightenment" and "The Scientific Revolution". It's important to note that this entire evolution is very Eurocentric, but at least for historiography this makes a lot of sense seeing as history as an academic discipline did mostly came into fruition in Europe.

Now, how meaningful all these markers and abstract terms actually are, that's up for debate. I think that it's important to keep in mind that these are the patterns and terminology we use to make sense of history. They are very much shaped by our thinking patterns and our modern day world view. It's simply impossible to seperate ourselves from our education and resulting thinking patterns. So when you look towards history written in ways that seem "inferior" to your expectations, try to keep that in mind. I'm by no means trying to say that all categorizations are meaningless or that our current methodology shouldn't be upheld, I'm merely trying to point out that we very much live within the bubble of our own time and culture.

Here is a book that gets at your question OP. Sort of the history of History type of thing. It was the first book they made us read when I started grad school.