Ehhh.... It depends on what you mean by human cognition. Usually when tech people are talking about cognition, they're just talking about a specific cognitive process in neurology.

Tech enthusiasts tend to present human cognition in a reductive manor that for the most part only focuses on the central nervous system. When in reality human cognition includes anyway we interact with the physical world or metaphysical concepts.

There's something called the mind body problem that's been mostly a philosophical concept for a long time, but is currently influencing work in medicine and in tech to a lesser degree.

Basically, it questions if it's appropriate to delineate the mind from the body when it comes to consciousness. There's a lot of evidence to suggest that that mental phenomenon are a subset of physical phenomenon. Meaning that cognition is reliant on actual physical interactions with our surroundings to develop.

I’d love to hear about any studies explaining the mechanism of human cognition.

You're just asking for any intro to cognitive psychology textbook.

At every step of modern computing people have thought that the human brain looks like the latest new thing. This is no different.

It's not specifically related, but biological neurons and artificial neurons are quite different in how they function. Neural nets are a crude approximation of the biological version. Doesn't mean they can't solve similar problems or achieve similar levels of cognition , just that about the only similarity they have is "network of input/output things".