Yes, there is a on-device Gemini model for Chrome. (Chrome Built-in AI), they have been testing it for over a year (been participating) and there were hackathons around it (ongoing until Nov 1 https://googlechromeai2025.devpost.com).

In general, I like the idea, but I'm afraid the final implementation will still auto-decide between using the local (for cost saving) and cloud LLM. And potentially outsourcing all your browser-usage LLMs calls to Big Tech like Google is a no-go .