Clang (and lld) do support native TLS, and mingw-w64 does have the things that are needed. I think binutils also might have what's needed too, but AFAIK the thing that's missing is support for it in GCC.

Actually, (upstream) Clang defaults to native TLS instead of emulated TLS. In MSYS2, Clang is overridden to use emulated TLS by deafult to interoperate better with GCC built code and libstdc++ though.

The toolchain I maintain, https://github.com/mstorsjo/llvm-mingw, defaults to native TLS throughout.