`double_ended_iterator_last` should not emit on move FnMut closure

Summary

This lint is not emitted on a non-move closure, but it fails to see the order dependence when the closure is marked as move.

Lint Name

double_ended_iterator_last

Reproducer

I tried this code: (playground)

(this is a little contrived, but it's a simplified version of the code I found it on)

#[deny(clippy::double_ended_iterator_last)]
fn find_best<'a>(a: &'a [usize], b: &[i32]) -> Option<(usize, &'a usize)> {
    let mut best_val = 0;
    a
        .iter()
        .enumerate()
        .rev()
        .filter(move |&(i, &val)| {
            match b[val].cmp(&best_val) {
                Ordering::Less => false,
                Ordering::Equal if i < val => false,
                Ordering::Equal | Ordering::Greater => {
                    best_val = b[val];
                    true
                }
            }
        })
        .last()
}

I saw this happen:

error: called `Iterator::last` on a `DoubleEndedIterator`; this will needlessly iterate the entire iterator
  --> src/main.rs:6:5
   |
 6 | /     a
 7 | |         .iter()
 8 | |         .enumerate()
 9 | |         .rev()
...  |
19 | |         })
20 | |         .last()
   | |_______________^
   |

I expected to see this happen:

No lint to be emitted, as what happens if the closure is made not move

Version

rustc 1.98.0 (88d9e12ae 2026-08-18)
binary: rustc
commit-hash: 88d9e12ae178fab0fb5cc050a94da85685d449ea
commit-date: 2026-08-18
host: x86_64-unknown-linux-gnu
release: 1.98.0
LLVM version: 22.1.8

Additional Labels

@rustbot label +I-suggestion-causes-bug

Start by running the reproducer in src/main.rs and inspect the double_ended_iterator_last lint's handling of the move FnMut closure around filter and last. Compare it with the non-move closure behavior. Done means the lint is not emitted for this order-dependent case while existing applicable cases remain covered.