We disable the ones that fire, so we can use -Werror. We can then
investigate each warning individually and see whether to fix it or to
keep silencing it.
Compiling as C++ changes nothing semantically, but ensures that we don't
break C++ compatibility while also retaining C compatibility.
C++ compatibility is useful for tooling and additional diagnostics and
analyses.
It is still C code, so still compatible with C compilers as well. This
change lets us see more clearly where implicit conversions occur by
making them explicit.