Jason Isbell sues Suno, but not for copyright infringement.
He filed the suit alongside Guy Forsyth, Eduardo Calle, and Camper Van Beethoven’s David Lowery. Interestingly, rather than filing a straightforward copyright case, the plaintiffs claim Suno imitates their voices and styles without permission. After a long intro that involves the Borg for some reason, the complaint says:

TL;DR
- Jason Isbell and other musicians are suing Suno.
- The lawsuit claims Suno imitates artists' voices and styles without permission.
- Plaintiffs allege Suno's claims about prompt limitations are false.
- Suno generated a song mimicking Jason Isbell's vocals and style when his name was used as a prompt.