Like you, I thought these pieces of software and data were little more than statistics-based text generators. But it turns out that this is a Category Mistake.
There was an argument made by Raphaël Millière in a recent Mindscape Podcast [1] with Sean Carroll that finally landed for me. He used the example that human beings are driven to eat and reproduce, so by that argument all humans are just eating and reproducing machines. "Ah! But we developed other capabilities along the way to allow us to be good at that!" And that's the point.
GPT-4, for example, is very very good at producing pleasing and useful output for a given input. It uses a simulated neural net to do that. Why would one assume that on the way toward becoming excellent at that task that a neural net wouldn't also acquire other abilities that we associate with reasoning or cognition? When we test GPT-4 for these things (like Theory of Mind) we actually find them.
"Ah hah!" you say, "Humans are set up to learn from the get go, and machines must be trained from scratch." However if you consider the entirety of our genetic legacy together with our childhoods, those are our equivalent "training" from scratch.
I don't think it can be easily dismissed that we're seeing something significant here. It's not human-level intelligence yet. Part of the reason for that is that human brains are vastly more complex than any LLM at the moment (100s of trillions of "parameters" in LLM-speak, along with other advantages). But we're seeing the emergence of something important.
[1] https://www.youtube.com/watch?v=aUJOcVPdDvg