[Feat][Router] Add per-model request latency histogram

[banlor]

Follow-up to #813. Per-model latency histogram observed at the router, with a status label so errors don't pollute the success-path tail.

Named vllm:request_latency_seconds (not e2e_*) on purpose - the engine already exposes vllm:e2e_request_latency_seconds and clobbering it would break existing dashboards. The router-side version also picks up the router-to-engine hop, so the two are complementary.

Out of scope, still on #699: per-model request count + resource indicators. Will follow up.

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[gemini-code-assist]

Code Review

This pull request introduces a new Prometheus histogram metric, request_latency_seconds, to track router-level request latency across different servers and models. The changes include the metric definition, its integration into the request processing flow for both successful and failed requests, and corresponding unit tests. However, a significant issue was identified where latency could be double-counted if an exception occurs during post-processing after a 'success' observation has already been recorded. Furthermore, the current implementation labels HTTP error responses (4xx/5xx) as 'success' if no Python exception is raised, which contradicts the goal of the metric. It is recommended to refactor the observation logic to ensure it executes exactly once per request and accurately reflects the response status.

[banlor]

fixed in latest push - observation moved to a single point in finally, and http 4xx/5xx now tag as error

[ruizhang0101]

LGTM