If you modify the work, that creates a derived work from whatever copyright the original works has, not a new work that is fully copyrightable.

As the article says in the Tl;DR at the top the code may be contaminated by open source licenses

> Agentic coding tools like Claude Code, Cursor, and Codex generate code that may be uncopyrightable, owned by your employer, or contaminated by open source licenses you cannot see