The short version is the copyright office says it is possible works by creative human authors using AI tools are partially copyrightable in many cases.
See also [1] mentioned in the framework linked by sibling comment, AI copyright is essentially a logical extension of this.
[1] https://en.wikipedia.org/wiki/Monkey_selfie_copyright_disput...
As a simple example, assume a specific LLM-based tool (like Google's own, or someone else's) happens to generate a social media mascot for you that looks a lot like the modern rendition of Mickey Mouse.
Let's see how long that creation flies as public domain because it came out of an AI (that almost certainly consumed a giant amount of content produced by Disney as part of its training).
If you want a specific tool, here is Elsa with a cigarette generated using Midjourney and more: https://journeyaiart.com/tag/Elsa .
But what happens if they MIX some of their own code with AI-generated code, is that combination then their copyright? With such combined output it would be very difficult to determine which part was created by human, which by AI, and which by AI but slightly modified by human.
In the domain of graphics the AI could put in some markers which tells the graphic is AI-generated, but with code that is probabaly not possible, code is code and can always be edited by humans.
A separate question is that if I use Claude to generate some code but then stamp the output with my copyright notice, am I doing something illegal?