Google-Extended is a control, specified in robots.txt, that lets a site manage whether its content is used to help develop and improve Google's generative AI models. It is separate from standard Googlebot indexing, so a site can remain in Google Search while opting out of generative AI use, or allow both.
For brands trying to maximize AI visibility, the usual choice is to allow Google-Extended, since Google's AI surfaces such as AI Overviews, AI Mode, and Gemini draw on Google's understanding of the web. Disallowing it can reduce how your content contributes to those experiences. The decision is a deliberate trade-off between visibility and control over AI use of your content.