All of the notable generative AI companies have policies that the won't claim copyright over your outputs.

They also frequently offer "liability shields" where their legal teams will go to bat for you if you get sued for copyright infringement based on your usage of their terms.

https://help.openai.com/en/articles/5008634-will-openai-clai...

https://www.anthropic.com/news/expanded-legal-protections-ap...

https://ai.google.dev/gemini-api/terms#use-generated