Zig itself doesn't cross compile C/C++ code, LLVM does the work for Zig.
> If you have a Rust project that depends on C code, you will have to put in some work if you want to compile it for a different target.
Rust is built on LLVM, and so its toolchain can also cross-compile C/C++ code. There are crates for that[0], and projects inspired by that idea[1].
> Give it some time, it will.
Given enough time mountains become valleys. Zig doesn't compile to C now; and won't be mature and field-tested for a decade or more.