feat: Agent Office — AI 에이전트 가상 오피스 (#2)

## Summary
- 2D 픽셀아트 가상 오피스에서 AI 에이전트(Stock, Music)가 실제 작업 수행
- FastAPI + WebSocket 실시간 상태 동기화 + 텔레그램 봇 양방향 알림/승인
- BaseAgent FSM (idle/working/waiting/reporting/break), 서비스 프록시 패턴
- Docker Compose 서비스 (port 18900) + Nginx WebSocket 프록시

## Changes (13 commits)
- Backend scaffold: config, db, models, Dockerfile
- WebSocket manager + Service proxy
- BaseAgent FSM + StockAgent + MusicAgent
- Telegram bot + Scheduler
- FastAPI main (REST + WS endpoints)
- Infrastructure: docker-compose + nginx
- Code review fixes: HTTPException, async polling, input validation

Reviewed-on: #2

agent-office/app/agents/base.py

@@ -0,0 +1,72 @@
+import asyncio
+import random
+import time
+from typing import Optional
+
+from ..config import IDLE_BREAK_THRESHOLD, BREAK_DURATION_MIN, BREAK_DURATION_MAX
+from ..db import add_log
+
+VALID_STATES = ("idle", "working", "waiting", "reporting", "break")
+
+class BaseAgent:
+    agent_id: str = ""
+    display_name: str = ""
+    state: str = "idle"
+    state_detail: str = ""
+    _idle_since: float = 0.0
+    _break_until: float = 0.0
+    _ws_manager = None
+
+    def __init__(self):
+        self._idle_since = time.time()
+
+    def set_ws_manager(self, manager):
+        self._ws_manager = manager
+
+    async def transition(self, new_state: str, detail: str = "", task_id: str = None) -> None:
+        if new_state not in VALID_STATES:
+            return
+        old = self.state
+        self.state = new_state
+        self.state_detail = detail
+
+        if new_state == "idle":
+            self._idle_since = time.time()
+        elif new_state == "break":
+            duration = random.randint(BREAK_DURATION_MIN, BREAK_DURATION_MAX)
+            self._break_until = time.time() + duration
+
+        add_log(self.agent_id, f"State: {old} -> {new_state} ({detail})")
+
+        if self._ws_manager:
+            await self._ws_manager.send_agent_state(self.agent_id, new_state, detail, task_id)
+            if new_state == "break":
+                await self._ws_manager.send_agent_move(self.agent_id, "break_room")
+            elif old == "break" and new_state == "idle":
+                await self._ws_manager.send_agent_move(self.agent_id, "desk")
+
+    async def check_idle_break(self) -> None:
+        now = time.time()
+        if self.state == "idle" and (now - self._idle_since) > IDLE_BREAK_THRESHOLD:
+            if random.random() < 0.5:
+                break_type = random.choice(["커피 타임", "잠깐 산책", "졸고 있음"])
+                await self.transition("break", break_type)
+        elif self.state == "break" and now > self._break_until:
+            await self.transition("idle", "휴식 완료")
+
+    async def on_schedule(self) -> None:
+        raise NotImplementedError
+
+    async def on_command(self, command: str, params: dict) -> dict:
+        raise NotImplementedError
+
+    async def on_approval(self, task_id: str, approved: bool, feedback: str = "") -> None:
+        raise NotImplementedError
+
+    async def get_status(self) -> dict:
+        return {
+            "agent_id": self.agent_id,
+            "display_name": self.display_name,
+            "state": self.state,
+            "detail": self.state_detail,
+        }