You're hitting on the most subjective part of this whole process. I've run into all of the issues you describe, and the question is ultimately: how do you define a story?

Your GOP primaries example is a good one. Let's say we have articles on Trump's legal issues, other articles on Pence's classified documents, and other articles on DeSantis and books. Now let's say all of these articles describe these things in the context of the 2024 GOP primaries. Is this one story called "GOP primaries"? Or three separate stories? You could make a case either way.

I've tuned the algorithm to split stories in a way that "looks about right" to me. That's subjective, but there's no way around it. This is an issue whether you're using an algorithm or doing this manually.

A related challenge is that story definitions may change over time. The classified documents story is a good example for this. Right now there are articles on Trump, Biden, and Pence all mishandling classified documents. The algorithm is categorizing all of them as the same story (fair enough).

But let's say that next week (just making this up), Trump gets indicted for it. Is that a separate story now? If so, how do you treat that? Do you retroactively split out the "Trump" portion of the "classified documents" story as though they were not the same story before? Do you show the classified documents story splitting into two? Do you just create a new story on the day the indictment happens? Currently, the algorithm is set up to do the first of these, but again, you could make a case for any of them.

All of this is to say that there is subjectivity involved in this process.