Then there are build systems that natively support Rust in addition to other languages and know how to plug them together [2] [3] [4]. If you're already using one of these existing tools, then you don't need to roll your own, you can plug it into your existing project.
Of course if you really are using Makefiles in C you're already living in the wild west, so it's on you to figure out how to add Rust to your projects in that case (or switch to a better build system).
[1]: https://doc.rust-lang.org/cargo/reference/build-scripts.html
[2]: https://bazelbuild.github.io/rules_rust/
Often a new language in a project would define an application boundary. So those would be different containers or services. I may deploy via container images, or an OS specific installer, etc. If we aren't crossing an application boundary I may use FFI. Sometimes I use https://rust-lang.github.io/rust-bindgen/ to smooth that over for C dependencies. There is also a nice concept called a build.rs file: https://doc.rust-lang.org/cargo/reference/build-script-examp.... There's also tools like: https://github.com/casey/just and https://sagiegurari.github.io/cargo-make/
I rarely use multiple languages with Rust. A lot of interpreted languages have bindings through crates and can go in to a project through Cargo (python, etc). If it involves JS/TS on desktop, I'm usually using Tauri for that. Guess it depends on the system?
Hopefully that helps. You can also still use a Makefile if you want I just haven't dealt with one in a long time.