One more example how to override warp's problem with having lowest priority for rejection::not_found (so it starts looking into other branches and often results in e.g. 405 METHOD NOT ALLOWED)

warp.rs

// Define custom error enum, 
pub enum Error {
    NotFound()
    // ... and any more errors here
}

// Make it castable to Rejection
impl warp::reject::Reject for Error {}

pub async fn handler() -> std::result::Result<impl Reply, Rejection> {
    let user = db::get_user(&db_pool, id).await?;
    match user {
        Some(user) => Ok(json(&UserUpdateResponse::of(user))),
        None => Err(Error::NotFound().into())
    }
}

pub async fn handle_rejection(err: Rejection) -> Result<impl Reply, Infallible> {
    let code;
    if err.is_not_found() {
        code = StatusCode::NOT_FOUND;
        message = "Not Found";
    } else if let Some(e) = err.find::<Error>() {
        match e {
            // On rejection we force this custom branch, not err.is_not_foun()
            Error::NotFound() => {
                code = StatusCode::NOT_FOUND;
                message = "Not Found";
            }
            _ => {
                code = StatusCode::INTERNAL_SERVER_ERROR;
            }
        }
    } else {
        code = StatusCode::INTERNAL_SERVER_ERROR;
    }

    Ok(code)
}