It’s not quite that simple - there may be minor things here and there that are copyrightable like the name. But anything purely prompt generated is fair game to be copied and reused.
It will be interesting to see this tested, but companies telling people AI is writing their software may be a liability in the not-to distant future.
(This is based on USCO opinions and congressional testimony: https://www.copyright.gov/ai/ . EULAs are different things, and may restrict rights otherwise granted by the law, etc., etc.)