When <basetyps.h> defines wchar_t, it must obey -f(no-)short-wchar by referring to __WCHAR_TYPE__ which may not be `unsigned short`. Similarly, windef.h defining NULL may need to use GCC's __null. Otherwise one-definition-rule problems arise depending on whether wine or libc headers are included first.
Implementing these by deferring to the C89-specified libc headers, (or msvcrt's versions with -mno-cygwin) ensures matching definitions.
Per the apparent concern about using <uchar.h> in windows headers...
If it helps, stddef.h is a gcc header, not a glibc one i.e., in C89 (and up) it's part of the "freestanding implementation". So even with a different libc (or no libc), this header should still be provided by the underlying compiler. The use of __need_* is GCC-specific, but if those don't work we'll still get the needed types, just maybe with some extras too.
C89 Section 1.7: A conforming freestanding implementation shall accept any strictly conforming program in which the use of the features specified in the library section ($4) is confined to the contents of the standard headers <float.h> , <limits.h> , <stdarg.h> ,and <stddef.h> .
And jacek pointed out in IRC that tchar.h already includes <wchar.h>. Not sure how I overlooked that, but I'll clean that up and send v2 patches once we agree on how to address with the char16_t part.