Source? I ~~googled~~ web searched your claim, and this paper, "Sycophantic Chatbots Cause Delusional Spiraling, Even in Ideal Bayesians", was the top result. It does conclude, as expressed in the Abstract:

We then show that in this model, even an idealized Bayes-rational user is vulnerable to delusional spiraling, and that sycophancy plays a causal role. Furthermore, this effect persists in the face of two candidate mitigations: preventing chatbots from hallucinating false claims, and informing users of the possibility of model sycophancy.

So, while I agree with your gist of 'chatbots are bad for people', I think you may have overstated your claim: That even ideally rational 'people' can get led into AI psychosis by sycophantic chatbots is not the same as bots "affecting regular people just as much as mentally unstable people", because mentally unstable people might be more vulnerable to this type of reality-warping influence. "No-one is safe" is different from "We all suffer equally".