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ChatGpt is finished training and doesn't update itself in any way. The current conversation is fed each time as additional context back when you ask additional questions.

Thanks for the clarification.

If the chat is published on the net, and becomes part of ChatGPT's future training data, I wonder whether ChatGPT could somehow become "aware" of it in a way that would change its subsequent behaviour?

No, starting a new chat it gives me again a (different) wrong answer.

I should add that I looked closer now at the transcript from yesterday, and the second answer it gave me after apologising was actually not correct, but correct enough for me to code it with the help of some actual API documentation.

State is only persisted per session, so no it will not learn globally. This is fairly important otherwise users could feed it false information.

You might get the correct answer on the second try, but that would be down to random seeds.