WebKit is a web browser, not a web content provider, so it can act as a desktop client (possibly enriching the functionality by using additional C++ code) for a web-served application but it will not act as a content server. Usually in such a situation you should provide a content server implemented in a technology of your choice (be it java, C++/Qt, python, php or some other language) that handles requests from clients and then you provide two separate client technologies that connect to that service and query it for functionality. One of the clients should be some kind of webpage server and the other would be the desktop client.
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