Add scheduler prefill queue wait breakdown

[RitwijParmar]

Motivation

Follow-up for #28047.

SGLang currently records total scheduler queue time, but that does not show whether high TTFT came from backlog before a request was considered or from budget pressure after the scheduler first tried to admit it.

This PR adds the missing scheduler-side split mentioned in the issue thread.

Modifications

• Add first_prefill_attempt_time to scheduler request time stats.
• Stamp it when PrefillAdder first considers a request.
• Split prefill queue time into prefill_queue_idle and prefill_budget_wait stages.
• Export the split through per-stage metrics, request traces, duration logs, and output metadata.
• Reset the first-attempt timestamp on retract and prefill retry resets.
• Add unit coverage for the split math, serialization, and retry reset behavior.
• Document the new metric and trace stages under docs_new/.

This does not duplicate the pre-scheduler timing work in #25933. It sits inside scheduler admission. It also does not change HiCache tier counters from #26976.

Accuracy Tests

Not applicable. This only adds timing instrumentation and metadata.

Speed Tests and Profiling

Not applicable. The hot path addition is one guarded timestamp write when a queued request is first considered, plus derived metrics when the request enters forward.

Checklist

• Add unit tests according to the contribution guide.
• Update documentation according to the contribution guide.
• Follow the SGLang code style guidance.
• Format your code according to pre-commit.
• Provide accuracy and speed benchmark results.

Local checks run:

• /Users/ritwij/.cache/codex-runtimes/codex-primary-runtime/dependencies/python/bin/python3 -m compileall -q python/sglang/srt/observability/req_time_stats.py python/sglang/srt/managers/schedule_policy.py test/registered/unit/observability/test_req_time_stats.py test/registered/unit/managers/test_prefill_adder.py
• uvx ruff check --extend-ignore E402 python/sglang/srt/observability/req_time_stats.py python/sglang/srt/managers/schedule_policy.py test/registered/unit/observability/test_req_time_stats.py test/registered/unit/managers/test_prefill_adder.py
• git diff --check

I could not run pytest locally because this checkout is not installed with SGLang dependencies in the current environment. System Python missed pybase64, and the bundled Python does not have pytest. I did run a lightweight stubbed check of the new SchedulerReqTimeStats math and metric calls.

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CI States

Latest PR Test (Base): ❌ Run #27657056151
Latest PR Test (Extra): ❌ Run #27657056150

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