Nope. Nope nope nopety #NOPE!
https://arstechnica.com/google/2025/09/google-announces-massive-expansion-of-ai-features-in-chrome/
"Gemini isn't limited to your current tab. #Google aims to make it possible to interact with other apps and tabs without leaving the current screen. When you invoke #Gemini in #Chrome, it can work with the content in all your open tabs, and it has connections to Google products like Calendar and #YouTube. It can also find links in your history based on a vague remembrance."