I think Rust is not particularly FP because it encourages using loops instead of recursion and “let mut” is quite idiomatic in my understanding. Those two characteristics are more relevant than the type system. For example, Scheme and Clojure don’t have type classes but are clearly FP because recursion and immutability are idiomatic.
In Rust, even though it is true that .map, .fold, .filter, and .zip exist, first of all they also exist in Python, and second, they need to be sandwiched between .iter and .collect unless one is working with iterators which makes the code noisier and pushes the needle toward loops.
The influence of OCaml and Haskell is clear though, and it makes the language more pleasant to use.