fix(tui): strip <think>…</think> tags from assistant content and route to reasoning panel

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).

ui-tui/src/lib/reasoning.ts

@@ -0,0 +1,50 @@
+const TAGS = ['think', 'reasoning', 'thinking', 'thought', 'REASONING_SCRATCHPAD'] as const
+
+export interface SplitReasoning {
+  reasoning: string
+  text: string
+}
+
+export function splitReasoning(input: string): SplitReasoning {
+  let text = input
+  const reasoning: string[] = []
+
+  for (const tag of TAGS) {
+    const paired = new RegExp(`<${tag}>([\\s\\S]*?)</${tag}>\\s*`, 'gi')
+    text = text.replace(paired, (_m, inner: string) => {
+      const trimmed = inner.trim()
+
+      if (trimmed) {
+        reasoning.push(trimmed)
+      }
+
+      return ''
+    })
+
+    const unclosed = new RegExp(`<${tag}>([\\s\\S]*)$`, 'i')
+    text = text.replace(unclosed, (_m, inner: string) => {
+      const trimmed = inner.trim()
+
+      if (trimmed) {
+        reasoning.push(trimmed)
+      }
+
+      return ''
+    })
+  }
+
+  return {
+    reasoning: reasoning.join('\n\n').trim(),
+    text: text.trim()
+  }
+}
+
+export const hasReasoningTag = (input: string) => {
+  for (const tag of TAGS) {
+    if (input.includes(`<${tag}>`)) {
+      return true
+    }
+  }
+
+  return false
+}