> You can now ask questions about the entire page you’re on right from the omnibox. Chrome can suggest relevant questions based on the context of the page to help you kickstart your search. You'll get a helpful AI Overview from Search right alongside the page, with the ability to ask follow-up questions in AI Mode, so you can get helpful information without leaving the page.

I've done the normal things to exclude my site from search. I would like this to not run on my site either.