A lot of the standard library and an extensive part of the community ecosystem lives and breathes mutation at both the edges and in the internals, something people normally would avoid when trying to stick with functional programming. Sure, some mutation is always needed, but Rust wouldn't be the first language I'd pick if I want to focus on functional programming for sure.

No, but it’s widely acknowledged that functional programming features are useful even in imperative languages. Almost every imperative language that isn’t C, Go, or Hare has them. Java, C#, JavaScript, Python, Ruby. You should take a look at all the functions available on iterators in Rust if you haven’t. The Rust community tends to prefer using iterators to express things like looping when possible, which is a more functional style.

Mutation within a single program flow is a well-known functional programming pattern, e.g. as supported by the ST feature in Haskell. Shared mutability is much harder to reason about, so is generally excluded and Rust implements it separately.