server: stream the answer past a stray </think> instead of holding it (#783)

[Flor1an-B]

Fixes #783.

Problem

fe2d3b0 (#678) guards against a tool-enabled model writing a second reasoning pass into the answer channel and closing it with a literal </think>. On the streaming path the guard holds all answer text back until a second </think>, a tool call, or the final chunk arrives. For the common single-pass case — thinking + tools, one reasoning block, then a plain answer with no tool call — none of those arrive until the end, so the whole answer is buffered and flushed at once. Streaming is dead (bisected to fe2d3b0 by @links486; reported against Open WebUI, which defaults to native tool calling).

Why the old guard can't stream

The routing of post-</think> text depends on whether a second </think> ever appears — a whole-stream property with no early deterministic signal. "Hold until proven" is correct but fundamentally cannot stream. This PR trades that: stream the answer as content in real time and simply drop any stray </think> so it never reaches the client. The #678 diagnostics make this safe to do inline — the tag is a single vocabulary token (never split across deltas, 0 split cases measured), the model never re-opens <think> (0 opening tags measured), and a partial trailing < is already held by text_stream_safe_limit().

Net effect vs the two prior states

• vs current main (blocking): streaming restored for every thinking+tools turn.
• vs pre-Streaming /v1/messages: a second literal think-close tag is emitted as answer text (ANTH_STREAM_TEXT has no close-tag handling) #678 (leaking): the stray tag is now suppressed rather than forwarded verbatim — strictly better. The residual is that in the now-rarer second-pass case (fe2d3b0 also fixed the tool-schema prompt that provoked it) the draft streams as content instead of landing in the reasoning channel. Given the impossibility of early detection, this is the streaming-side tradeoff for real-time output.

Applied identically to the OpenAI (/v1/chat/completions) and Anthropic (/v1/messages) streams.

Testing

• The two fe2d3b0 guard tests are updated to the new semantics and renamed (*_suppresses_second_think_tag).
• Two regressions added (*_streams_answer_incrementally) assert content is emitted mid-stream, before the final chunk.
• Negative control: reverting the production hunk fails both new assertions (st.sent_content and the content-routing check), so the tests genuinely pin the regression.
• ./ds4_test --server green; warning-free ds4-server build on Apple M5 Max (Metal).

End-to-end, M5 Max / Metal / DeepSeek-V4-Flash resident, streaming /v1/chat/completions with a tool defined and thinking on, on a prompt the model answers directly (the case #783 regressed):

reasoning deltas : n=23  first=1.487s last=1.981s
content   deltas : n=43  first=2.003s last=2.957s
[DONE] at        : 2.957s
content started  : 0.954s BEFORE [DONE]   (was: single burst at [DONE])
content spread   : 0.953s across 43 deltas

Trace confirms the guarded path (tool-schema prompt injected, <think>…</think> then a plain answer, no tool call); output contained no stray </think>.

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