Are there any documents describing how to convert existing doxygen generated documents into the form supported by libhover?
The main website seemed to suggest that eventually doxygen might be supported, but I'm not sure what the status of that is. I noticed that the source code contains BuildFunctionInfos class which takes in "URL or file name of xml document to parse" and outputs the corresponding serialized LibHoverInfo, but I don't see any hints on what form the xml document should be.
No, there isn't. The BuildFunctionInfos is for C documentation that has been pre-formatted into the standard C library xml format as found in the header for glibc docs and newlib docs (you can download these directly from the URLs found in the respective libhover glibc and newlib plugins).
The libstdc++ libhover plugin includes a src directory which contains the doxygen converter that takes the libstdc++ doxygen documentation and produces the binary output. If your C++ documentation is in a similar format, it should be usable with only minor changes required.