Ms Johanssen is on shaky ground.
Neither copyright, patent, or trade secret applies. At best she *might* have standing to sue under publicity rights but first she has to prove her voice is unique and the synthetic voice is near identical to hers. Now, if they were claiming the synthetic voice is hers or if it were her appearance she would have a strong case, in *some* localities, under right of publicity.
www.law.cornell.edu
Even unfair competition is unlikely to get her a trial unless she has licensed her voice for use in software.
Depending on how her voice was used in HER--direct or processed--Spike Jonze might have a stronger case but even that might be a reach.
There is quite a bit of case law involving voice impersonators and pretty much all revolves around attributing the voice to a celebrity. If OpenAI makes no such claim, the onus falls on Johanssen.
Without going too far think of INDIANA JONES AND THE GRRAT CIRCLE. Harrison Ford has no case no matter how close Troy Baker mimics him. Neither woud he if they used a software voice clone because using software to do what is legal for humans to do is not per se illegal no matter how much it might annoy some.
LLMs are here and going nowhere.
And anybody expecting politicians to make it go away have a loooonnng wait ahead. Longer than a lifetime, in fact.