Add timings to server responses

[spicyneuron]

Adds a timings object to /v1/chat/completions and /v1/completions responses so clients can measure prompt and generation throughput without instrumenting the server themselves. Useful for benchmarking, comparing models, and surfacing tps in UIs.

The shape mirrors llama.cpp's timings field for ecosystem compatibility:

"timings": {
  "prompt_per_second": 412.3,
  "predicted_per_second": 78.9,
  "prompt_n": 128,
  "predicted_n": 64
}

Behavior

Follows the existing usage conventions:

• Non-streaming: always included.
• Streaming: included in the final usage chunk when stream_options.include_usage is set.

Implementation notes

• Measured server-side; reusing GenerationResponse.prompt_tps doesn't work because batched generation has no per-sequence equivalent.
• Both windows are stamped in the generation worker: prompt = prefill start → first generated token; predicted = first → last generated token. Excludes network I/O and pre-worker queue wait; includes a small amount of batch-tick overhead, so values are approximate.
• prompt_n excludes cached tokens. predicted_per_second is 0 when fewer than two tokens are generated.
• Includes a minor fix: streaming usage check uses .get("include_usage") instead of ["include_usage"] to avoid KeyError when stream_options is passed without that key.