Compiling Mesa with X in custom prefix fails in Intel Vulkan driver

We're currently testing compilation of X11 and Mesa into a custom prefix. For that we set PKG_CONFIG_PATH respectively, but compilation still fails:

In file included from ../../source/include/vulkan/vk_icd.h:10,
                 from ../../source/src/vulkan/runtime/vk_object.h:27,
                 from ../../source/src/vulkan/runtime/vk_acceleration_structure.h:28,
                 from ../../source/src/intel/vulkan/anv_private.h:73,
                 from src/intel/vulkan/grl/grl_metakernel_misc.h:26,
                 from src/intel/vulkan/grl/grl_metakernel_misc.c:26:
../../source/include/vulkan/vulkan.h:71:10: fatal error: X11/extensions/Xrandr.h: No such file or directory
   71 | #include <X11/extensions/Xrandr.h>
      |          ^~~~~~~~~~~~~~~~~~~~~~~~~
compilation terminated.

According to @whot's analysis this seems to be a Mesa bug as the correct cflags are not pulled from xrandr.pc. See this comment for more info.