As of now, iOS does not have a built-in feature that allows the AssistiveTouch menu circle to automatically hide when a mouse is not connected. The AssistiveTouch menu circle is designed to be a persistent on-screen feature that offers accessibility shortcuts for users who rely on assistive tools, such as those using a mouse, trackpad, or touch alternatives. The primary goal of AssistiveTouch is to provide easy access to system controls, gestures, and actions for users who may have difficulty with traditional touch gestures.
Even if such a feature existed, automatically hiding the circle when a mouse is disconnected could undermine the very purpose of AssistiveTouch. The menu circle serves as a constant visual cue for users who depend on it for navigation, and removing it when no mouse is connected could potentially make it harder for them to access the assistive features when needed, especially if they regularly toggle between using the mouse and other assistive methods. This would compromise the accessibility benefits by making the interface less predictable for those who rely on it.