Our goal is to build this locally— there's even some heuristics we've found (i.e clicking the same items in a row every time you visit a website) that can give really good completions without an LLM.
Chrome is even starting to ship a small Gemma model in the browser, but we haven't seen great performance from Gemma yet.
But yes, and I have the same concerns w/ this, code completions, Grammerly etc. Hopefully all these tools will follow the same trajectory (some usage with a cloud setup -> distilled into a small local setup).