Adapts Qwen3-Omni PD disaggregation to current config-refactor

[spencerr221]

Purpose

This PR adapts Qwen3-Omni PD (prefill-decode) separation to the new config-refactor flow introduced by #2383, without adding a new deploy YAML.

It adds pd_separation support to the deploy-based config pipeline so the existing vllm_omni/deploy/qwen3_omni_moe.yaml can dynamically expand the original 3-stage Qwen3-Omni pipeline into a 4-stage PD layout at merge time. When enabled, the thinker stage is split into prefill and decode stages, downstream stage IDs and connectors are remapped, and KV transfer settings are injected from deploy config.

This keeps the new pipeline+deploy model intact, preserves the existing PD detection/runtime logic, and avoids introducing a separate PD-specific config file after the config refactor.

Test Plan

Test Result

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[amy-why-3459]

Can you add PD separation performance test cases?

[hsliuustc0106]

please update the docs as well

[hsliuustc0106]

BLOCKING:

• Gate Check — pre-commit is failing. Please fix pre-commit issues before proceeding with review.

[hsliuustc0106]

BLOCKING:

• Gate Check — pre-commit still failing (end-of-file-fixer on test_qwen3_omni_expansion.py, E501 line too long in stage_config.py:757, ruff format). Please run pre-commit run --all-files locally and push the fix.

Non-blocking:

• PR description Test Plan / Test Result sections are empty. Please add CI results or local run output showing the PD expansion tests pass (e.g. test_pd_disaggregation.py, test_config_factory.py::test_merge_pipeline_deploy_with_pd_disaggregation).