Provide way to handle a request with a MethodRouter without requiring an exclusive reference

[cdhowie]

• I have looked for existing issues (including closed) about this
  • Possibly related to Can state be cloned less when handling requests? #1827 and Avoid some extra clones/allocations #2865.

Feature Request

Motivation

When writing a Service implementation that wraps a MethodRouter, and when the wrapping service's call method needs to do some async work before forwarding the request to MethodRouter, there is no way to avoid cloning the entire MethodRouter (or putting it behind a mutex, which is almost certainly worse). This is because MethodRouter does not expose any way to handle a request without a &mut MethodRouter, and futures returned by Service::call (understandably) cannot capture &mut self.

Proposal

Adding a method to MethodRouter that routes a request with a &MethodRouter would allow the wrapping service to hold an Arc<MethodRouter>. Changing MethodRouter::call_with_state from pub(crate) to pub would resolve this, though whether this is the correct way to resolve this request is likely a question better answered by the axum maintainers.

Alternatives

Any other approach that allows me to route a request using a &MethodRouter would be totally acceptable.