Google-Extended is not a separate crawler with its own user agent; it is a control you set in robots.txt to opt your content in or out of Google's AI training and grounding uses.
Because it is decoupled from Search ranking, blocking Google-Extended does not protect or harm your blue-link rankings. AI Overviews are fed by ordinary Googlebot, not Google-Extended, so blocking the token does not remove you from AI Overviews either. It only governs Gemini training and grounding, so weigh AI visibility against training concerns when deciding.