> formal proofs are, as Rust provides something very similar to that

Since when? Rust just has an ML-like type system, and seemingly many have met that for the first time with Rust, even though it has decadeS of history, and multiple production languages running it just fine (ocaml, scala, etc).

Formal proofs are way way above an ML type system. Like how do you encode mathematical statements in Rust's type system? What about statements about program semantics, like program A is equivalent to program B <- in formal verification THAt is the type of an expression, and the implementation of it is the proof.