Investigate if Windows and Linux need something OS specific (e.g something resembling Universal links or App Links).

At a quick glance it would appear that Windows and Linux don't have similar in-app callback mechanisms. Rather there'd need to be a "QSingleApplication" type of forwarder application. That application would be launched when an URL handling is due, and if the application notices there's already an instance running, it would forward the data there. In addition an installer on Windows would need to modify registry, and on Linux we'd need a .desktop file.

However, the above is just a very quick look into this. In any case, the findings should be documented into the URI scheme handler "platform support" documentation.