I'm not convinced—and certainly don't find it obvious—that this couldn't ultimately also be how we reason as humans.

It's clear that there's an enormous amount of leverage built into language-as-practiced that one can use to engage in a broad spectrum of reasoning, from the extremely fallible off-the-cuff conclusion to the deeply-considered and rigorous proof. How do we know this leverage is built into language-as-practiced? Because LLMs can do a broad swath of it.

But how do we know we're not doing something similar?

I don't think we can assume that we're not simply by observing that we're not digital and we don't use matrix multiplication. Why immediately dismiss the possibility that there might be a similar, but biomechanical, computation at play in our heads that plays in the same space of vectors?