Use cargo-c instead of cmake

[cargo-c](https://github.com/lu-zero/cargo-c) exists exactly to ease the build of Rust programs into C libraries, it's an easier and less error-prone approach than managing the cmakefiles yourself.

Start by reviewing the repository's current CMake-based build setup and how Rust programs are exposed as C libraries, then compare the required integration with cargo-c. Done means the supported C-library builds work through cargo-c without the existing manually managed CMake approach.

Written by the indexing model from the issue text.