Instead of:

private static void qsort_with_data<T> (T[] elems, size_t size, [CCode (type = "GCompareDataFunc")] GLib.CompareDataFunc<T> compare_func);

It should be:

private static void qsort_with_data<T> (T[] elems, size_t size, [CCode (type = "GCompareDataFunc")] GLib.CompareDataFunc<T *> compare_func);

Currently to sort array of strings (as an example) one need to do:

qsort_with_data<string> (sorted_data, sizeof(string), (a, b) => {return strcmp(*(string **)a, *(string **)b);});