No, it really doesn't. That's you asking it about it's thinking and it responding. That's different than reflection, which would consist of it asking itself anything about its thinking.

It doesn't seem to be reflecting on its own thinking so much as reflecting on the output it's already generated. It can't look back at its prior thought process and go "D'oh! What was I thinking?", but it can look at the program it just printed out and find the error.

But it seems to me that ChatGPT is just not built to look at its own "cognition", that information just shouldn't be available to it. Each time it answers a prompt it's just reading back through the entire conversation as though it's never seen it before; it doesn't remember generating the responses in the first place.

I can't be sure but I would guess that the only way ChatGPT even knows that it's an AI called ChatGPT in the first place is because OpenAI explicitly built that knowledge into it*. It doesn't know about its own capabilities by performing self-reflection - it's either got that information built into it, or it's inferring it from its training data (for instance, it may have learned general facts about language models from its training data and would know, given that it itself is a language model, that those facts would apply to itself).

*EDIT: I looked it up and in fact the reason it knows these things about itself is because it was fine-tuned using sample conversations in which human beings roleplayed as an AI assistant. So it doesn't know what it is through self-reflection; it essentially knows it because it learned by example how to identify itself)

It's probably going to devolve into a semantics debate.

ChatGPT model neurons stay the same until they retrain it and release a new version.

But, you feed it back its own output + more prompt, and now it has extra context about the ongoing conversation.

For now I would have to say it shouldn't be described as "reflecting on its own thinking", since each turn is independent from others and it's simply trying to predict what would've been reasonable to appear in text. For example: It could be an interview in a magazine, etc.

That being said... I'm a big fan of the saying that AI doesn't need human-brain-style thinking to achieve a working imitation of human-level intelligence, just like the airplane is an example of flying without imitating the bird.

Nope, that's just its prediction of what string of characters corresponds to your prompt.