Just an idea but Nim seems to have the features you mentioned. Nim "transpiles" to C, and can even be compiled via `zig cc` (which is an interace to clang). If you really want to, maybe you could make a zig backend for Nim?
Popularity is one thing { and probably more people use it than a non-existing new PLang you are only at the design phase of :-) }, but I think you misunderstood the backend idea. Nim has a javascript backend via `nim js` and on that backend you can use `emit` to do inline javascript, just as on the C/C++ backends you can use emit to put out C/C++. So, if you did do a zig backend, being able to emit inline zig would be part of that. It may still not be what you want, of course.