Wrong inferred `impl FnMut()`

rust-analyzer version: 0.3.1748-standalone (237712fa3 2023-11-26)
rustc version: 1.74.0

rust-analyzer infers wrong type for closure, rustc says it only implements FnOnce, but RA shows impl FnMut

struct Int(i32);
impl Int {
    fn change(&mut self) {
        self.0 += 1;
    }
}
let mut int = Int(0);

// RA: impl FnMut()
let foo = move || {
    async move {
        int.change();
    };
};

fn is_it_fn_mut(_val: impl FnMut()) {}
is_it_fn_mut(foo); // rustc error

rustc error:

Start by reproducing the minimal closure example in the issue with the specified rust-analyzer and rustc versions, then compare the inferred impl FnMut() with rustc's FnOnce result. The issue is done when rust-analyzer reports the closure's inferred trait consistently with rustc for this case.