HUD: hover and tooltips for moved windows

Windows poll the mouse cursor object (0xcdbadc, x +4) for hover; it is
shifted inside a moved window's render/event scope like the events.
Tooltips are separate windows placed by the hovered window in its 1024
layout, so cUI_Tooltip renders with the offset of the moved window under
the cursor. Adds Move-To to the test input helpers.

Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com>

tools/game-input.ps1

@@ -75,3 +75,13 @@ function Save-Screen([string]$Path, [int]$Width = 3440, [int]$Height = 1440) {
     $graphics.Dispose(); $bitmap.Dispose()
     $full
 }
+
+# Moves the cursor in small steps (the game only sees real mouse movement).
+function Move-To([int]$X, [int]$Y, [int]$AfterMs = 800) {
+    [SacredRe.Input]::SetCursorPos($X - 20, $Y - 20) | Out-Null
+    for ($i = 1; $i -le 10; $i++) {
+        Start-Sleep -Milliseconds 20
+        [SacredRe.Input]::SetCursorPos($X - 20 + 2 * $i, $Y - 20 + 2 * $i) | Out-Null
+    }
+    Start-Sleep -Milliseconds $AfterMs
+}