Out of curiosity, do you have a ChatGPT Plus subscription, but no (trial) OpenAI API key?
For the OpenAI Mathematica notebook features (including chat) to work you need an OpenAI API key. You can get a key to use the API in a trial for 3 months (with a max rate and max $5, but it can get you far enough).
The ChatGPT Plus subscription and the OpenAI API are billed separately. The ChatGPT Plus subscription covers usage exclusively on the chat.openai.com platform and costs $20 per month, providing benefits such as general access even during peak times, faster response times, and priority access to new features and improvements.
On the other hand, the OpenAI API has its own separate pricing structure. It allows developers to integrate the OpenAI models, including ChatGPT, into their own applications or software. The API usage is billed based on the number of API calls made and the amount of tokens processed. The API usage is not covered by the ChatGPT Plus subscription, and it requires a separate subscription and separate payment.