We actually recently published a research paper on exactly this topic (see https://llm-privacy.org/ for demo and paper). The paper shows that current LLMs already have the reasoning capability to infer personal attributes such as age, gender or location even when this information is not explicitly mentioned in the text. Crucially, they can do this way cheaper and way faster than humans. So I would say that spying scenarios mentioned in this blog post are definitely in the realm of possibility.