I now think it's likely I misunderstood what the feature involves and that it is actually way more limited than I thought compared to CopilotKit (perhaps it's little different from Gmail's Smart Compose), but this is a quick-and-dirty screenshot:
This looks like a very rudimentary completion, almost Markov chain level. I don't think it requires sending user data to any remote servers, it could have easily been done on the client.