[SSE Completion - Issue 2] Prior-turn reasoning leaks <think> into the visible answer

[ashwing]

Part of #118.

On a multi-round gateway tool session, raw <think>...</think> markup appears in the client's visible output_text channel (while reasoning also streams correctly on its own reasoning_text channel). Customer sees think-tags inside the final answer.

Root cause (localized with layered vLLM-direct vs gateway tests): the Continue branch in executor/engine.rs calls append_output_items_to_input(&mut ctx.enriched_request.input, &current_output), and OutputItem::to_input_item maps Reasoning → InputItem::Reasoning (types/io/output.rs:390). So each round feeds the previous round's reasoning item back into inference; the qwen3 reasoning parser then re-emits it wrapped in <think> on the visible channel.

vLLM is not at fault — it's clean unless a prior reasoning item is in the input history:

Test (vLLM-direct)	<think> in output_text
single turn	no
round-2 with function_call + output, no reasoning	no
round-2 with round-1 reasoning fed back	yes
round-2 reasoning excluded	no (fix confirmed)

Fix: don't carry prior-turn reasoning items into subsequent inference rounds — reasoning is ephemeral per-turn. Scope the fix to the loop's Continue carry-forward (filter Reasoning out of the append_output_items_to_input(&current_output) call) rather than changing to_input_item globally — the latter is also used on the client-action / previous_response_id continuation paths, where whether reasoning should round-trip is a separate question worth not disturbing here. The excluded-reasoning test confirms the leak vanishes and the answer stays correct.