Handling error layer / converting fallible services/layers to infallible

[lcmgh]

Axum provides https://docs.rs/axum/0.7.5/axum/error_handling/struct.HandleErrorLayer.html

Example use case:
Respond with too many requests http status code in case ConcurrencyLimitLayer is not ready.

let concurrency_layer = LoadShedLayer::new().layer(ConcurrencyLimitLayer::new(100));

This did not work for me

let handle_error_layer = HandleErrorLayer::new(handle_concurrency_error); // from axum

async fn handle_concurrency_error(
    // `Method` and `Uri` are extractors so they can be used here
    method: Method,
    uri: Uri,
    // the last argument must be the error itself
    err: tower::BoxError,
) -> (StatusCode, String) {
    (
        StatusCode::TOO_MANY_REQUESTS,
        format!("`{method} {uri}` failed with {err}"),
    )
}

let concurrency_layer = LoadShedLayer::new().layer(ConcurrencyLimitLayer::new(100));


Server::builder()
    .layer(handle_error_layer)
    .layer(concurrency_layer)

Error:

   --> src/lib.rs:144:10
    |
144 |         .serve(addr)
    |          ^^^^^ the trait `tower::Layer<SetSensitiveRequestHeaders<SetSensitiveResponseHeaders<tower_http::trace::Trace<Routes, SharedClassifier<GrpcErrorsAsFailures>, {closure@src/lib.rs:94:25: 94:53}>>>>` is not implemented for `LoadShed<ConcurrencyLimitLayer>`, which is required by `Stack<LoadShed<ConcurrencyLimitLayer>, Stack<HandleErrorLayer<fn(Method, Uri, Box<(dyn std::error::Error + Send + Sync + 'static)>) -> impl Future<Output = (http::StatusCode, std::string::String)> {handle_concurrency_error}, _>, tower::layer::util::Identity>>: tower::Layer<SetSensitiveRequestHeaders<SetSensitiveResponseHeaders<tower_http::trace::Trace<Routes, SharedClassifier<GrpcErrorsAsFailures>, {closure@src/lib.rs:94:25: 94:53}>>>>`

Originally posted by @lcmgh in #1934

How could this be achieved?