> Seeing is an inferior means of knowing where the cursor is compared to intuition. When I move the cursor, I know where it is with no conscious effort [...]

Realize it consciously or not, visual feedback is a critical part of this loop.

> As soon as the off-screen action finishes, the mouse cursor snaps back to the position it would have otherwise been in.

The cursor jumping to the edge of the screen, which is not somewhere the user ever saw it and may be outside of the application, seems worse than any current issue while still being insufficient for most legitimate use-cases.

I don't really see any fake cursor approach that isn't going to behave awkwardly in practice - e.g: is it your real (invisible?) cursor or fake cursor that can click to focus another application, and what happens to your cursors when you do so?

Just letting the user deny mouse control for an app (like on Wayland) seems sufficient to solve your annoyance. Maybe adding a separate permission for control while unfocused, since that's rarer. No need to break all windowed applications with reason to capture/move the mouse.