I'm not sure about licenses that explicitly forbid LLM use -- although you could always modify a license to require this! -- but GPL licensed projects require that you also make the software you create open source.
I'm not sure that LLMs respect that restriction (since they generally don't attibute their code).
I'm not even really sure if that clause would apply to LLM generated code, though I'd imagine that it should.
They don't require it if you don't include OSS artifacts/code in your shipped product. You can use gcc to build closed source software.
Very likely no license can restrict it, since learning is not covered under copyright. Even if you could restrict it, you couldn't add a "no LLMs" clause without violating the free software principles or the OSI definition, since you cannot discriminate in your license.