Mouse cursor hide-on-type breaks if mouse recently moved

### Windows Terminal version

1.13.10395.0

### Windows build number

Version 10.0.19043.1586

### Other Software

_No response_

### Steps to reproduce

When typing in windows terminal the mouse cursor hides. However if you move the mouse cursor and then type without waiting long enough, even if you don't move the mouse cursor at all any more, the mouse cursor instead hides, and then after a couple of seconds unhides itself.

Expected behavior:

### Expected Behavior

Mouse cursor hides and stays hidden when you type.

Or (unlikely) if an earlier recent move is intended to prevent hiding, then just prevent hiding rather than hide/unhiding.

### Actual Behavior

If you type after a recent mouse move, the cursor hides itself and then after a delay unhides itself, even if there was no mouse movement after the hide.

If you type after a less recent mouse move (the threshold seems to be > 1-2 seconds), things work correctly: the cursor hides and stays hidden.

Start by reproducing the cursor behavior on the reported Windows Terminal and Windows versions, then trace the terminal's mouse-movement and typing-related cursor visibility handling. Done means typing shortly after moving the mouse hides the cursor without a later unexplained reappearance, including when there is no subsequent mouse movement.

Written by the indexing model from the issue text.