I'm not aware of a text lawsuit either, but there is one for code:
https://githubcopilotlitigation.com/. I'm a little surprised there isn't one for text yet, since the Washington Post published an article detailing how many tokens from websites, including those run by major media companies, go into large models:
https://www.washingtonpost.com/technology/interactive/2023/a.... It may be that corporations think they can profit off these models to a greater extent than they are subject to damages, that their attorneys simply don't think they have a case, or that they want to see how the image and code lawsuits go first. This is all speculation, however.