Projects cannot allow AI generated code if they require everything to have a clear author, with a copyright notice and license.

IDE code suggestions come from the database of information built about your code base, like what classes have what methods. Each such suggestion is a derived work of the thing being worked on.

That is not correct because it hasn't been tested in court. In past decisions about who owns the output generated by a computer program the owner has been the operator of the program. You own your Word documents and Photoshopped images. There is good reason to believe that LLM output where you provided the prompt would also fit under that umbrella. We are still waiting for that to be tested in court.