I urge you to actually read the article, because it doesn't say anything about the risks of the LLM knowing your password (e.g., stored in server-side logs), it talks about LLMs generating predicatable passwords because they are deterministic pattern-following machines.

While the loss of secrecy between you and the LLM provider is a legitimate risk, the point of the article was that you should only use vetted RNGs to generate passwords, because LLMs will frequently generate identical secure-looking passwords when asked to do so repeatedly, meaning that all a bad actor has to do is collect the most frequent ones and go hunting.

The loss of secrecy between you and the LLM only poses a risk if the LLM logs are compromised, exposing your generated passwords. The harvesting of commonly-generated passwords from LLMs poses a much broader attack surface for anyone who uses this method, because any attacker with access to publicly available LLMs can start mining commonly generated passwords and using them today without having to compromise anything first.