Google separates AI-training consent from Search crawling. Googlebot crawls for Google Search; blocking it removes you from Search. Google-Extended is a robots.txt-only control governing whether the content Google already crawls may be used to train future Gemini models and for grounding.
The reassuring part
Per Google's documentation, Google-Extended does not impact a site's inclusion in Google Search nor is it used as a ranking signal. So you can disallow Google-Extended to opt out of Gemini training while keeping full Google Search visibility. Note Google-Extended has no separate request user-agent string — Googlebot performs the fetch — so a live user-agent probe can't test it; robots.txt is the control surface. Confirm current details on Google's official page.