From what I've read, it seems that "chatbot addiction" would be more accurate than "AI psychosis" ... if for some reason the name for this thing had to be an analogy to an existing psychiatric condition.
Consider what the person is doing physically. They're sitting in front of a machine that feeds them variable reinforcement, and spending way too much of their time and attention on engaging with that machine, to the detriment of their human attachments like family, friends, or work. That looks a lot more like a problem gambler's or porn addict's behavior, than like a schizophrenia patient's behavior.
In this view, the content of the user's dialog with the chatbot isn't central: it doesn't much matter if it's romantic fantasy, crank physics, or religion. The "delusions" are flavor, like whether a particular drinker prefers wine, margaritas, or hazy IPAs; or which model of slot machine a gambler favors; or what kink the porn addict is into.
I'm curious what else we might call the phenomenon, though.
I think chatbot addiction is a different issue. I think what people are usually pointing out when they talk about AI psychosis are phenomena where (like the post says) people become delusional, or their delusions seem to be shaped by exposure to the chatbot. My sense is that there's also a related phenomenon where people might become less mentally stable and more likely to take violent actions that they wouldn't have otherwise considered, even if they had the false beliefs that they now have, but idk if that's right
What is psychosis
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.
The most important symptoms of psychosis
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.
What do people mean when talking about 'AI psychosis'
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.
Why 'AI psychosis' is an unhelpful label
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.
What could we call it instead
Something like 'AI enforced delusions' would avoid confusion with psychosis related medical conditions like schizophrenia.