> I wasn't aware that CPython builds for MSYS2 out of the box, since it's a POSIX-on-Windows platform like Cygwin. Apparently there are patches that enable it to build, since MSYS2 has Python available.

MSYS2 consists of a cygwin like environment and a mingw one. OP is trying to build with mingw.

MSYS2 contains a somewhat heavily patched Python in both environments so it's expected that building plain CPython doesn't work. There are plans to upstream smaller non-MSYS2 specific patches but nothing has come of it so far.