If you looked at the link you included you'd see why the Rust version is larger, because they include the static library.

There's nothing about Rust that intrinsically makes it larger than C.

My problem with Lua and MicroPython is that your actual code takes up memory, ie even comments. Micropython can now compile to bytecode and load that, though, so it's better. I've had problems with Lua trying to load one or two hundred lines, though.