You may also be banned by asking "sensitive" or "inappropriate" questions. So normal usage of Google AI products could also be risky.

I don't care if my Claude or OpenAI account is banned, but risking a Google account is different.

Does that apply to the search AI too?

I don't know but I'm basing my assumptions on this article: Teenager’s Gemini mistake locks entire family out of Google accounts [1].

1. https://www.pcworld.com/article/3104521/teenagers-gemini-mis...