glibc qsort's implementation is in libc.so, not in the header. GCC doesn't have anything to work with.
It's also an apples-to-oranges comparison, since std::sort and qsort implement different algorithms.
A lot of std::sort's performance is actually from using the version without any callbacks. If you pass a comparator function which just compares two integers the obvious way, it gets much slower. So one of std::sort's biggest advantages is actually not that it uses templates, but that it's specialized for the common case of not needing a custom callback. Theoretically the compiler should make the two cases the same, but apparently GCC is too dumb (that's not a slight on GCC; I think people expect too much from compilers):
------------------------------------------------------------------------
Benchmark Time CPU Iterations
------------------------------------------------------------------------
std_sort_random 52881299 ns 52873089 ns 14
std_sort_with_callback_random 63319633 ns 63307876 ns 11
qsort_random 106803314 ns 106784567 ns 7
external_sort_random 97642851 ns 97640888 ns 7
std_sort_sorted 8433311 ns 8432564 ns 82
std_sort_with_callback_sorted 13868016 ns 13865170 ns 50
qsort_sorted 28098439 ns 28093720 ns 26
external_sort_sorted 33629020 ns 33628108 ns 21
external_sort is just
std::sort hidden behind an extern function implemented in a separate .o file. Those benchmarks are from sorting 1MB of random and already-sorted data (as indicated in the names). I think it's important to test such cases, because often online people benchmark code which is written all in a single file, whereas real-life C++ projects are usually organized in such a way that every little class is in its own little file, which gets compiled into a separated object file, and then it all gets linked together without LTO. And then those same people go on to claim performance benefits of their language without actually using the setup which enables those benefits, which IMO is a bit dishonest.
When I drill further down into everything I want to drill into, maybe I'll publish the source for the benchmarks somewhere.