Rust code can have arbitrary I/O effects in any parts of it. This precludes using only Rust's type system to make sure code does what spec said.
The most successful formally proven project I know, seL4 [1], did not extracted executable code from the proof. They created a prototype in Haskell, mapped (by hand) it to Isabelle, I believe, to have a formal proof and then recreated code in C, again, manually.
Not many formal proof systems can extract executable C source.