needless_pass_by_ref_mut: false negative with fn and closures

Summary

No clippy warning for needless_pass_by_ref_mut when both wrapping fn and closure have mutable args.

Discovered while working on https://github.com/rust-lang/rust/pull/123188

checked with clippy from playground 0.1.79 (2024-03-27 c9f8f34)
https://play.rust-lang.org/?version=nightly&mode=release&edition=2021&gist=047b73855da451dd617b8d43557b8d0d

Lint Name

needless_pass_by_ref_mut

Reproducer

I tried this code:

#![warn(clippy::needless_pass_by_ref_mut)]

fn main() {}

fn foo(n: &mut u8)->u8 {
    let x = |c: &mut u8| *c;
    x(n)
}

fn foo2(n: &mut u8)->u8 {
    let x = |c: &u8| *c;
    x(n)
}

fn foo3(n: &u8)->u8 {
    let x = |c: &u8| *c;
    x(n)
}

I expected to see this happen:
For foo should warn about unused &mut in fn args and closure. Probably should first warn about closure arg, because if closure fixed, it will successfully warn about fn args (as in foo2)

Instead, this happened:

No warn for foo

Version

No response

Start by locating the needless_pass_by_ref_mut lint entry point and its existing tests, then run the Rust reproducer from the issue. Done means the foo case reports the unnecessary mutable references, with the closure argument diagnosed before the wrapping function argument as described.