feat(agent-office): 텔레그램 자연어 대화 + 프롬프트 캐싱 + 평가 지표

- 슬래시 명령이 아닌 메시지를 Claude Haiku 4.5로 응답
- system 프롬프트 + 히스토리 끝 블록에 cache_control:ephemeral 적용
- conversation_messages 테이블에 토큰·캐시·latency 기록
- chat_id 화이트리스트 + 분당 rate limit
- GET /api/agent-office/conversation/stats 로 캐시 히트율·토큰 확인

agent-office/app/db.py

@@ -67,6 +67,25 @@ def init_db() -> None:
                 created_at  TEXT NOT NULL DEFAULT (strftime('%Y-%m-%dT%H:%M:%fZ','now'))
             )
         """)
+        conn.execute("""
+            CREATE TABLE IF NOT EXISTS conversation_messages (
+                id              INTEGER PRIMARY KEY AUTOINCREMENT,
+                chat_id         TEXT NOT NULL,
+                role            TEXT NOT NULL,
+                content         TEXT NOT NULL,
+                model           TEXT,
+                tokens_input    INTEGER DEFAULT 0,
+                tokens_output   INTEGER DEFAULT 0,
+                cache_read      INTEGER DEFAULT 0,
+                cache_write     INTEGER DEFAULT 0,
+                latency_ms      INTEGER DEFAULT 0,
+                created_at      TEXT NOT NULL DEFAULT (strftime('%Y-%m-%dT%H:%M:%fZ','now'))
+            )
+        """)
+        conn.execute("""
+            CREATE INDEX IF NOT EXISTS idx_conv_chat
+            ON conversation_messages(chat_id, created_at DESC)
+        """)
         # Seed default agent configs
         for agent_id, name in [
             ("stock", "주식 트레이더"),
@@ -319,6 +338,109 @@ def get_token_usage_stats(agent_id: str, days: int = 1) -> dict:
     }
 
 
+def save_conversation_message(
+    chat_id: str,
+    role: str,
+    content: str,
+    model: Optional[str] = None,
+    tokens_input: int = 0,
+    tokens_output: int = 0,
+    cache_read: int = 0,
+    cache_write: int = 0,
+    latency_ms: int = 0,
+) -> None:
+    with _conn() as conn:
+        conn.execute(
+            """
+            INSERT INTO conversation_messages
+                (chat_id, role, content, model, tokens_input, tokens_output,
+                 cache_read, cache_write, latency_ms)
+            VALUES (?,?,?,?,?,?,?,?,?)
+            """,
+            (str(chat_id), role, content, model, tokens_input, tokens_output,
+             cache_read, cache_write, latency_ms),
+        )
+
+
+def get_conversation_history(chat_id: str, limit: int = 20) -> List[Dict[str, Any]]:
+    """최근 N개를 시간순(오래된 → 최신)으로 반환."""
+    with _conn() as conn:
+        rows = conn.execute(
+            """
+            SELECT role, content FROM conversation_messages
+            WHERE chat_id=? ORDER BY id DESC LIMIT ?
+            """,
+            (str(chat_id), limit),
+        ).fetchall()
+    return [{"role": r["role"], "content": r["content"]} for r in reversed(rows)]
+
+
+def count_recent_user_messages(chat_id: str, seconds: int = 60) -> int:
+    with _conn() as conn:
+        r = conn.execute(
+            """
+            SELECT COUNT(*) AS c FROM conversation_messages
+            WHERE chat_id=? AND role='user'
+              AND created_at >= strftime('%Y-%m-%dT%H:%M:%fZ','now', ?)
+            """,
+            (str(chat_id), f"-{int(seconds)} seconds"),
+        ).fetchone()
+    return r["c"] if r else 0
+
+
+def get_conversation_stats(days: int = 7) -> Dict[str, Any]:
+    with _conn() as conn:
+        rows = conn.execute(
+            """
+            SELECT chat_id,
+                   COUNT(*) AS msg_count,
+                   SUM(tokens_input)  AS in_tokens,
+                   SUM(tokens_output) AS out_tokens,
+                   SUM(cache_read)    AS cache_read,
+                   SUM(cache_write)   AS cache_write,
+                   AVG(latency_ms)    AS avg_latency
+            FROM conversation_messages
+            WHERE role='assistant'
+              AND created_at >= strftime('%Y-%m-%dT%H:%M:%fZ','now', ?)
+            GROUP BY chat_id
+            """,
+            (f"-{int(days)} days",),
+        ).fetchall()
+
+    by_chat = []
+    tot_in = tot_out = tot_r = tot_w = tot_msgs = 0
+    for r in rows:
+        ci = int(r["in_tokens"] or 0)
+        co = int(r["out_tokens"] or 0)
+        cr = int(r["cache_read"] or 0)
+        cw = int(r["cache_write"] or 0)
+        mc = int(r["msg_count"] or 0)
+        hit_rate = (cr / (cr + cw)) if (cr + cw) > 0 else 0.0
+        by_chat.append({
+            "chat_id": r["chat_id"],
+            "message_count": mc,
+            "tokens_input": ci,
+            "tokens_output": co,
+            "cache_read": cr,
+            "cache_write": cw,
+            "cache_hit_rate": round(hit_rate, 3),
+            "avg_latency_ms": round(float(r["avg_latency"] or 0), 1),
+        })
+        tot_in += ci; tot_out += co; tot_r += cr; tot_w += cw; tot_msgs += mc
+
+    overall_hit = (tot_r / (tot_r + tot_w)) if (tot_r + tot_w) > 0 else 0.0
+    return {
+        "days": days,
+        "total_messages": tot_msgs,
+        "tokens_input": tot_in,
+        "tokens_output": tot_out,
+        "cache_read": tot_r,
+        "cache_write": tot_w,
+        "cache_hit_rate": round(overall_hit, 3),
+        "by_chat": by_chat,
+    }
+
+
 def get_activity_feed(limit: int = 50, offset: int = 0) -> dict:
     with _conn() as conn:
         total_row = conn.execute("""