feat: show per-stage timing (듣기/LLM/TTS) in the transcript channel

The transcript channel only showed STT and LLM seconds. Add wall-clock
start/end times and durations for listening, LLM and TTS so it's obvious
what takes long; STT surfaces as the gap between listening end and LLM start.

- bridge: emit llm_start_ms/llm_end_ms on meta and tts_*_ms on the end event
- bot: capture the listening window, assemble full timing after the stream,
  and render a per-stage breakdown in the transcript message

Co-Authored-By: Claude Opus 4.7 <noreply@anthropic.com>

bot/src/userbot.ts

@@ -34,12 +34,66 @@ async function loadSelfbot(): Promise<any> {
   }
 }
 
-interface TurnInfo {
+export interface TurnInfo {
   transcript: string;
   reply: string;
   note?: string;
-  sttSec?: number;
-  thinkSec?: number;
+  /** Wall-clock epoch-ms markers for each pipeline stage. STT is the gap
+   *  between listenEndMs and llmStartMs. */
+  listenStartMs?: number;
+  listenEndMs?: number;
+  llmStartMs?: number;
+  llmEndMs?: number;
+  ttsStartMs?: number;
+  ttsEndMs?: number;
+}
+
+/** Local wall-clock HH:MM:SS for an epoch-ms instant. */
+function clock(ms?: number): string {
+  if (ms == null) return "?";
+  const d = new Date(ms);
+  const p = (n: number) => String(n).padStart(2, "0");
+  return `${p(d.getHours())}:${p(d.getMinutes())}:${p(d.getSeconds())}`;
+}
+
+/** Seconds between two epoch-ms instants, 1 decimal, or null if either side is
+ *  missing or the span is negative (clock skew / out-of-order markers). */
+function durSec(a?: number, b?: number): string | null {
+  if (a == null || b == null) return null;
+  const s = (b - a) / 1000;
+  if (s < 0) return null;
+  return s.toFixed(1);
+}
+
+/** Build the transcript-channel message: transcript + reply, plus a per-stage
+ *  timing breakdown (listening / LLM / TTS) with start→end wall-clock times and
+ *  durations, so it's obvious what took long. Pure + exported for testing. */
+export function formatTurnMessage(info: TurnInfo): string {
+  const head = info.transcript
+    ? `🎤 들음 → 🗣️ "${info.transcript}"\n🤖 답변: ${(info.reply || "").trim() || "(무응답)"}`
+    : `🎤 들음 → ❌ ${info.note || "무시됨"}`;
+
+  const lines: string[] = [];
+  const listen = durSec(info.listenStartMs, info.listenEndMs);
+  if (listen != null) {
+    lines.push(`   👂 듣기 ${listen}초  ${clock(info.listenStartMs)} → ${clock(info.listenEndMs)}`);
+  }
+  const llm = durSec(info.llmStartMs, info.llmEndMs);
+  if (llm != null) {
+    const stt = durSec(info.listenEndMs, info.llmStartMs);
+    const gap = stt != null && Number(stt) >= 0.1 ? `  (STT/전송 ${stt}초)` : "";
+    lines.push(`   🧠 LLM ${llm}초  ${clock(info.llmStartMs)} → ${clock(info.llmEndMs)}${gap}`);
+  }
+  const tts = durSec(info.ttsStartMs, info.ttsEndMs);
+  if (tts != null) {
+    lines.push(`   🔊 TTS ${tts}초  ${clock(info.ttsStartMs)} → ${clock(info.ttsEndMs)}`);
+  }
+
+  if (!lines.length) return head;
+  const lastEnd = info.ttsEndMs ?? info.llmEndMs ?? info.listenEndMs;
+  const total = durSec(info.listenStartMs, lastEnd);
+  const totalNote = total != null ? ` (합계 ${total}초)` : "";
+  return `${head}\n⏱️ 타이밍${totalNote}\n${lines.join("\n")}`;
 }
 
 /** Mirror EVERY heard utterance (and why it did/didn't answer) to a text
@@ -47,17 +101,7 @@ interface TurnInfo {
 async function postTranscript(client: AnyClient, info: TurnInfo): Promise<void> {
   const chId = config.transcriptChannelId;
   if (!chId) return;
-  const timing =
-    info.sttSec != null || info.thinkSec != null
-      ? `  ⏱️ stt ${info.sttSec ?? "?"}s · llm ${info.thinkSec ?? "?"}s`
-      : "";
-  let msg: string;
-  if (info.transcript) {
-    const r = (info.reply || "").trim();
-    msg = `🎤 들음 → 🗣️ "${info.transcript}"\n🤖 답변: ${r || "(무응답)"}${timing}`;
-  } else {
-    msg = `🎤 들음 → ❌ ${info.note || "무시됨"}${timing}`;
-  }
+  const msg = formatTurnMessage(info);
   try {
     const ch: any = await client.channels.fetch(chId).catch(() => null);
     if (ch?.send) await ch.send(msg);