RoxyRoxyRoxy
No. That suggestion was very good, but I'm thinking an indicator in the gray bar at the top of the assistant (the one where it says model, Entire Web, Attach, Temporary, [+], and the hamburger menu that applies to the currently selected model.
I was thinking immediately to the right of the [+] put a little status indicator that shows the privacy of the currently selected model (like a VPN shows a connected icon to signify you're private)
Red: Not private
Yellow: Primarily private but not on fallback server
Green: Private
The indicator could also serve as a button to enforce privacy instead of just indicating it. So click the indicator and it turns blue and blocks all models from running that aren't fully private.
I think the key is having the option to block all models which aren't private, but doing it with a little privacy indicator switch seems like a slick way of doing it. It's also a constant reminder that you provide privacy whereas others may not.