[Feature]: Establish baseline and profile fish-speech's performance

🚀 The feature, motivation and pitch

As we continue to optimize vllm-omni, we want to establish a clear performance baseline for the fish-speech-S2 model. To know exactly "where we are at" and how much room we have for improvement, we are looking for community help to benchmark our current implementation against a great community reference like sglang-omni.

Our primary goal is internal profiling. Even if our current metrics are slower, it is a crucial step for us. Comparing with other excellent frameworks will help us identify our specific bottlenecks (e.g., scheduling overhead, memory management, or operator efficiency) and understand why we are slower, which will guide our next steps in optimization.

Tasks:

• Set up the testing environment for vllm-omni and sglang-omni as a reference.
• Run the same fish-audio inference workload on both to collect baseline metrics (e.g., TTFT/Time To First Audio, RTF, Throughput).
• (Optional but highly appreciated) Provide a basic profiling breakdown if you notice where vllm-omni might be lagging.
• Share the reproducible scripts and environment details.

Who can help: This is a great good first issue for anyone interested in TTS serving performance! The community's enthusiasm is what keeps us moving forward. If you have some bandwidth to help us find our bottlenecks, we would greatly appreciate your contribution! 🙌

Alternatives

No response

Additional context

cc: @ywang96 @hsliuustc0106

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