Makes you wonder whether the affiliate links are actual, valid affiliate links or just hallucinations from affiliate links it's come across in the wild

It clearly is a 100% custom UI logic implemented by OpenAI… They render the products in carrousels… They probably get a list of product and brand names from the LLM (for certain requests/responses) and render that in a separate UI after getting those affiliate links for those products… its not hard to do. Just slap on your affiliate ID to the links you found and you are done.