Unable to find pthread.h for mingw32 on nix

Question

I'm trying to cross-compile a program which uses pthreads to windows using nix and mingw. The build complains about missing headers (pthread.h), even though i set windows.pthreads as a buildInput.

windows.pthreads seems to only copy libpthreadGC2.a and ignore the headers. (source)

win.nix:

{ pkgs ? import (builtins.fetchTarball "https://github.com/nixos/nixpkgs/archive/nixos-23.05.tar.gz") { } }:
let
  source = pkgs.writeText "main.c" ''
    #include <pthread.h>

    int main() {
      return 0;
    }
  '';
  package = { runCommandCC, fetchurl, stdenv, windows }: runCommandCC "test" {
    buildInputs = [ windows.pthreads ];
  } ''
    mkdir $out
    cd $out

    cd $out
    $CC -pthread ${source} -o main
  '';
in
  pkgs.pkgsCross.mingw32.callPackage package { }

Compilation:

nix-build win.nix
this derivation will be built:
  /nix/store/7cwz7v404nm51i34avfqpvzz4mm2r7mb-test-i686-w64-mingw32.drv
building '/nix/store/7cwz7v404nm51i34avfqpvzz4mm2r7mb-test-i686-w64-mingw32.drv'...
/nix/store/11635lqa2ad8225ahky756pmj5fv81kl-main.c:1:10: fatal error: pthread.h: No such file or directory
    1 | #include <pthread.h>
      |          ^~~~~~~~~~~
compilation terminated.