The documentation says:
Note that WinSCP actually disables “move” by default, so you have probably enabled it before.
The Allow moving from remote directory to other applications checkbox is by default disabled allowing you to only copy files using drag&drop.
Despite this, dragging a file from the remote panel into a Windows Explorer window (not the local panel) will MOVE the file from the server. It is a new WinSCP installation; all settings are on default. The mouse cursor even shows the + sign, suggesting it will be a copy. But still, the actual operation was a move
The fix for this problem was to change from "Use shell extension" to "Use temporary folder" (leaving the "Allow moving from remote directory to other applications" checkbox still disabled).
After doing that, the drag would only copy the file, it no longer "moves" by having WinSCP delete the file on server.
P.S.: Is it not possible for WinSCP to simply ignore whatever Windows Explorer tells it and just leave the server file alone after copying it out (even when using shell extension)? The explanations given suggest that WinSCP will always be a slave to Explorer's commands and do what Explorer tells it to do - but WinSCP is a standalone program - it can make its own decisions. So I don't get that rationale.