This is one of the shining features of the language: either of these is a viable option. Zig is a great way to build C projects, with native cross-compiling, and the semantics make it straightforward to supply a C API for Zig libraries to add to existing code in C. Depending on the specifics, it can make sense for a C codebase to switch to Zig's build system just for excellent cross compilation, without writing anything in Zig.
I think once Zig stops being a moving target, we'll see an increasing number of C codebases writing some of the new code in Zig, moving over to the build system, and taking it from there. There are a lot of decisions which make this easy. As an example, idiomatic Zig code which allocates memory receives an Allocator, where C uses malloc and free. So there's a C allocator, which provides the Allocator interface to malloc and free, meaning Zig code can create objects and pass the memory to C, which can free it later.
There's a lot of C code out there which is working just fine, and if it ain't broke, no need to fix it. But if it's easy to do new work in a nicer language (to my taste, Zig is definitely that), why not? Then maybe rewrite some preprocessor-heavy C code using comptime.
The main thing holding this back (though it's already happening) is that Zig is pre-1.0. That imposes a maintenance burden which not everyone is willing to take on. But that won't last forever.