Minimal example reproducing axum compilation problem

Cargo.toml

[package]
name = "minimal_axum"
version = "0.1.0"
edition = "2021"

[dependencies]
axum = { version = "0.6.1" }
tokio = { version = "1", features = ["full"] }

main.rs

use std::sync::{Arc, Mutex};

use axum::{extract::State, routing::get, Router};

#[tokio::main]
async fn main() {
    let state = Arc::new(Mutex::new(AppState::default()));

    let app = Router::new()
        .route("/", get(example_handler))
        .with_state(state);

    axum::Server::bind(&"0.0.0.0:3000".parse().unwrap())
        .serve(app.into_make_service())
        .await
        .unwrap();
}

#[derive(Default)]
struct AppState;

impl AppState {
    async fn other(&self) {}
}

async fn example_handler(State(state): State<Arc<Mutex<AppState>>>) {
    let state = state.lock().unwrap();
    state.other().await // without async/await, this compiles
}