Models that emit reasoning inline as <think>/<reasoning>/<thinking>/<thought>/
<REASONING_SCRATCHPAD> tags in the content field (rather than a separate API
reasoning channel) had the raw tags + inner content shown twice: once as body
text with literal <think> markers, and again in the thinking panel when the
reasoning field was populated.
Port v1's tag set to lib/reasoning.ts with a splitReasoning(text) helper that
returns { reasoning, text }. Applied in three spots:
- scheduleStreaming: strips tags from the live streaming view so the user
never sees <think> mid-turn.
- flushStreamingSegment: when a tool interrupts assistant output mid-turn,
the saved segment is the stripped text; extracted reasoning promotes to
reasoningText if the API channel hasn't already populated it.
- recordMessageComplete: final message text is split, extracted reasoning
merges with any existing reasoning (API channel wins on conflicts so we
don't double-count when both are present).
