Clippy `contains_key` followed by `insert` suggestion won’t compile

Summary

From https://users.rust-lang.org/t/clippy-contains-key-followed-by-insert-suggestion-wont-compile/100243

Clippy's suggestion of replacement code doesn't compile

See Playground 1

Reproducer

I tried this code:

use std::collections::BTreeMap;

#[derive(PartialEq, PartialOrd, Eq, Ord, Clone, Copy, Debug)]
struct Pos(usize, usize);

fn can_get_to(start: Pos, end: Pos) -> Option<u32> {
    if start == Pos(1,1) && end == Pos(2,2) {
        Some(5)
    } else {
        None
    }
}

fn main() {
    let mut distance: BTreeMap<Pos, u32> = BTreeMap::new();
   
    let posnear = Pos(1,1);
    let posfar = Pos(2,2);
    
    distance.insert(posnear, 10);
   
    if !distance.contains_key(&posfar) {
        if let Some(dist) = can_get_to(posnear, posfar) {
          distance.insert(posfar, distance[&posnear] + dist);
        }
    }
    
    // Clippy's suggestion for above - won't compile
    // if let std::collections::btree_map::Entry::Vacant(e) = distance.entry(posfar) {
    //     if let Some(dist) = can_get_to(posnear, posfar) {
    //         e.insert(distance[&posnear] + dist);
    //     }
    // }

    dbg!(distance);
}

And the compile error from Clippy's suggestion:

error[E0502]: cannot borrow `distance` as immutable because it is also borrowed as mutable
  --> src/main.rs:31:22
   |
29 |     if let std::collections::btree_map::Entry::Vacant(e) = distance.entry(posfar) {
   |                                                            ---------------------- mutable borrow occurs here
30 |         if let Some(dist) = can_get_to(posnear, posfar) {
31 |             e.insert(distance[&posnear] + dist);
   |               ------ ^^^^^^^^ immutable borrow occurs here
   |               |
   |               mutable borrow later used by call

Version

No response

Additional Labels

@rustbot label +I-suggestion-causes-error

Start by locating the Clippy lint that emits the contains_key/insert suggestion, then compile the supplied BTreeMap reproducer to confirm the failure. Done means the suggested replacement compiles while preserving the intended insertion behavior, with a regression test covering the reproducer.