[hnyls2002]

The scheduler has no owner for "running": the running requests are spread over running_batch, last_batch, the overlap result copies and the PP micro-batches, and a request just prefilled lives only in last_batch until the next merge. This adds an owner list kept at state transitions. Nothing reads it yet; later PRs move the readers (abort targets, the running timeout, the weight-version inventory, the idle check) to it.

• Add RunningReqs (scheduler_components/running_reqs.py), owned by the scheduler as running_reqs: the running requests in join order (join, leave, leave_finished), rebound as a new dict on every change so iterating while requests leave is safe.
• A request is running once its whole prompt is launched, until it finishes; the steps still computing for it are tracked apart. It joins when a launched step runs its last prefill chunk (run_batch, and the MLX overlap launch): the extend or mixed step's requests other than its chunked request and any finished row. A step composed before the previous result is processed (overlap off, e.g. a DP-converted decode step) can still carry a row that result finished; it must not join. _prefill_launch_starts_running() says when a launch does not start a request running: a PD prefill request goes to the KV transfer, a PD decode request starts when the prebuilt batch is merged, a HiSparse one when _build_hisparse_decode_batch merges it after staging, and a dLLM one never runs.
• A request leaves when it finishes (at the end of process_batch_result: running requests finish only while a step is processed), when retract_decode retracts or aborts it, when priority preemption takes it, and when a retract-mode pause retracts it (under PP that pause covers only the current micro-batch).
• PP keeps one list for all micro-batches.
• SGLANG_ENABLE_RUNNING_REQS_CHECK (on by default in CI, like SGLANG_ENABLE_TREE_CACHE_SANITY_CHECK; off otherwise) makes SchedulerInvariantChecker.maybe_check_running_reqs run at each schedule, after the merge and filter. It checks that the list equals the unfinished requests the batches hold (running_batch and last_batch, every micro-batch under PP), apart from the chunked request. When a prefill launch does not start a request running, extend step batches are left out of that set.
• Add test_scheduler_running_reqs.py: launch joins through the real run_batch (chunked, mixed, decode, and the modes that skip it), an overlap sequence through the real get_next_batch_to_run with the check on, and the retract and preemption leaves. test_scheduler_dp_converted_batch_full.py runs with the check on; unit fakes that reach the hooks get the list.

No behavior change.

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CI States

Latest PR Test (Base): 🚫 Run #41177278010
Latest PR Test (Extra): 🚫 Run #41177278023
Latest PR Test (AMD ROCm 10): 🚫 Run #41177277979

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