This happened to me too. Not 'Claude code' as such but I was doing some I guess slightly grey area scraping (of an undocumented public API) and got my IP address blacklisted. I signed up for some rotating residential proxies to get around that, and then noticed that the scraping system Claude had built for me 'helpfully' added my email address as a user-agent.
It mentioned that it decided to do this so that they could reach out to me and ask questions instead of blocking me again, but still probably one of the strongest cases of misalignment I've seen from an AI