Generative AI, meaning models which imitate existing digital artifacts and media isn't what all this is about. This was an attempt to find a common name for both #LargeLanguageModel chatbots and to generative image/video/sound models in wide use now. It's a descriptive label which looks to the past.
The next generation of these systems won't be imitative, but they will be trained in self-competition as agents. It's not about them generating content based on examples, it is about surpassing human cognition in agents making decisions. We already use #agentic architectures when we deploy LLMs. It's still the same tech though, a natural next step, not something radically different.
LLM chatbots weren't made to be assistants or chatbots, they were made to measure the intelligence of the underlying deep neural network. It comes from #AGI tech, not from generative models. That is the correct umbrella term for these technologies, at least as they apply to #automation and surpassing human intellectual and cognitive limits.