Setting a custom hardware cursor does not work unless the mouse cursor re-enters the active game window

We are having this issue in 4.19.2. Within the default editor viewport launch mode, there is no issue. But using either the “Standalone game” launch mode, or cooking the whole project, leads to the cursor being initially the default windows cursor, and if the cursor exits the window and comes back in, to our custom hardware cursors.

Fortunately my project is easily simplifiable to a small size (1.4MB zipped). Is there anywhere I can pass it down to you without making it public here?