If, after entering the OpenAI API Key, and the system informs you of an error «Model "gpt-4o-mini" not active», you need to enable «gpt-4o-mini» model.

Navigate to OpenAI Settings page. 

Click on the «Limits» tab.

Be sure to enable the «gpt-4o-mini0187 model in the model list section:

After enabling the desired model, generate the API key again.

Now everything works.