Feature request: move mouse to the selected window

[xalt7x]

This feature will be helpful for multiple monitors, ultra-wide monitors, and generally when the user needs to input periodically on multiple tiled windows.

We already had a few GNOME extensions that move the cursor to the center of the focused window:

1. Mouse follows focus. This one with the "remember last position of cursor inside previous window" PR worked nicely.
   The only issue I've had is that when I close the window on one monitor, the cursor sometimes moves to the active window on another monitor. And so movement only after Alt+Tab/Super+Tab Applications/Windows switching seems less intrusive.
2. Alt-Tab Move Mouse. This one didn't remember the position on a previous window, so I used the first one until GNOME 45 was released.

So, for me, it would be perfect to:

1. Move the cursor only after switching to non-maximized windows using:
   a. Window switcher (Alt+Tab or whatever user/distro sets)
   b. App switcher (Super+Tab or Alt+Tab if Window Switcher is unset)
   c. App window switcher (Super+Above_Tab, Alt+Above_Tab)
2. Have some position history because, during frequent switching, it could be annoying to always move the cursor from the center/header of the window input position.