Even if you're not an adversarial government leaning on it as a hacking enhancement, it's only a matter of time till governments worldwide demand certain controversial conversational topics be reported to law enforcement. I suspect the Knight Paladins of Anthropic would be more than eager to further this greater cause for the Safety of mankind.
From the start, since all but a few services are using your data to improve their models there is already no notion of privacy. The ethical ones will eventually (if not already) report suspicious activity (as determined by law) to law enforcement and the less ethical ones will report all activity to advertising and insurance agencies.
Some already lobby to ban opensource AI because enhancing the learning rate and reducing the friction of gaining new information for humanity without controlling oversight will also enhance hackers or other bad actors ability to access sanctioned knowledge. They consider this a heresy and deem humanity at large incapable of responsibly handling such increases in cognitive ability. Only a few Adept can be trusted with administering AI. Truly, spying is among the more trivial concerns for the future of computing, given AI's compute heaviness and the amount of centralizing control it engenders by default.