If there's a configured and local Syncthing connection and we're on a
non-UNIX platform which doesn't support SIGTERM (basically Windows) it
makes sense to use the REST-API instead. That's likely better than just
terminating the process forcefully.
This doesn't cover the stop button within the launcher settings yet because
from this context is isn't clear which connection is relevant as there can
be multiple tray icons/widgets but only one settings page.