feat: Distributed tracing for router

[gaocegege]

To evaluate the router's performance, it would be useful to support distributed tracing. This would allow us to track the end-to-end latency from the router all the way to the vLLM inference, helping us identify the sources of latency.

Related: https://opentelemetry.io/docs/concepts/signals/traces/

[YuhanLiu11]

Would be nice to have this feature! 😄

(cc @ApostaC)

[Sozhan308]

Hi @gaocegege,

I noticed the task for OpenTelemetry integration for tracing. I'd be happy to contribute to this effort if you're looking for support. Let me know if you'd like me to take it on.

[ApostaC]

@Sozhan308 Please feel free to do it! Really appreciate your contribution!