Psychosis is a syndrome (a collection of often disparate symptoms) that includes thinking problems, delusions, hallucinations, and negative symptoms. People with psychosis often present very differently. Most crucially, you can have psychosis without delusions, if you have other core symptoms such as hallucinations and disorganised thinking.
Delusions and hallucinations are often seen as the 'core' symptoms of psychosis. This is because they are the most dramatic, but also because they are the symptoms that can be treated by antipsychotics, which led to the first dopamine theory of psychosis. However, impacted cognition and negative symptoms are often more serious in terms of their impact on functioning. Some in the psychosis research community argue that cognition is the core symptom of psychosis Schizophrenia is a cognitive illness: time for a change in focus - PubMed.
Some academics in psychiatry have begun to talk about how AI may exacerbate psychosis. What I don't think has been suggested is that AI can cause psychosis in those who would not have developed the disorder. To know this you would need (at least) longitudinal data, which isn't available due to the recency of chatbot use.
It is quite unlikely that chatbot use can cause the brain dysconnectivity that is evidenced to be a neural substrate of psychosis. It is also unlikely that AI chatbot use can cause the dopaminergic neural bases of psychosis. Rather, when examples are given of people believing unusual things because of chatbot use we are either seeing someone developing a set of beliefs that are unusual enough to be considered delusions, which is not psychosis, or someone who is developing psychosis whose delusions are shaped by chatbot use.
AI psychosis as a phrase suggests both that delusions are the core (and sometimes only) symptom of psychosis and that chatbots could cause serious mental illness, for which there is no evidence.
Something like 'AI enforced delusions' would avoid confusion with psychosis related medical conditions like schizophrenia.