Human authorship?

At least in NL law, the copyright belongs to the person that made the creative choices. In other words, no AI tool can ever produce anything copyrightable by itself. The user who made the creative choices that lead to the output has the copyright. This is the same principle that prevents Microsoft from claiming copyright over your Word documents, or a compiler writer claiming copyright over your binaries.

If those companies somewhere in the chain include a human who is deciding which AI output is acceptable and which isn't, then that would be copyrightable. Even if they were just writing a program that did the evaluation for them. Although I expect the actual protection to be somewhat commensurate to the amount of effort. And if you're talking to a chatbot, the output is copyright of the person typing.

This is Civil Law, so by statute and no court case can change that. At best the courts can prod the legislature to tell them the law might need updating, but that's it. The US being Common Law however is likely to attract a lot of litigation, unless the legislature explicitly goes to fix it.