Other than having to know Rust, adding Rust to a C code base is not difficult. They play well together.

There is no need to rewrite old code but, once Rust is there, you are free to.

Linux is a bit of a special case as you cannot just blindly use the Rust standard library.

Having to have a Rust tool chain to build with may or may not be an issue.

For some use cases, like BSD or the Linux kernel, platform support is also a consideration.