Mouse automatically moves with active window

[Xionical1]

Moving windows with 'Focus follows mouse' option (or other) will cause subsequent shortcuts to act on a different window due to a different window gaining focus upon moving.

Whenever moving a window using hotkeys I would like an option for the mouse to snap to (by default) the center of the window. Or perhaps the same position relative to where it was before the move.

I could just enable 'Click to focus' but I like the focus following the cursor when I am using it.

I might be able to use some other script that moves the cursor to the last active window, and bind that to a shortcut, but that is super clunky and seems like a waste to not implement it here.

Hopefully this is possible. If not I understand, as wayland more or less makes it difficult to take control of the users inputs.
I also looked at the api, and it seems like there is no official way to change the mouse position. However with ydotool you can move the mouse. See here.

Thank you for your consideration.