bugfix: defer streaming chat role chunk until generation starts

[amd-youchen]

Motivation

The streaming chat handler sent the role: "assistant" chunk as soon as the
request was accepted, before the engine produced anything.
That is not what OpenAI does -- the first chunk is supposed to mean generation
has actually started (vLLM emits it on the first iteration of the result
generator). It also skews client-side metrics: a chat client that times the
first SSE chunk without checking for content records a near-zero TTFT and
counts the real first token as an inter-token latency. The /v1/completions
benchmark path has no such chunk, so existing numbers are unaffected, but the
chat path is a trap for external clients.
This PR defers the role chunk until the first engine chunk arrives, for both
the single-sequence and n>1 fanout paths. It still precedes any content or
tool_calls delta, so client-visible ordering is unchanged.

[github-actions]

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