feat: NanoClaude 프로덕션 통합 — Docker, Caddy, aiosqlite 로깅

- docker-compose에 nanoclaude 서비스 추가 (포트 8100)
- Caddy /nano/* → nanoclaude 리버스 프록시 (SSE flush)
- aiosqlite 요청/응답 로깅 (request_logs 테이블)
- .env.example, CLAUDE.md 업데이트

Co-Authored-By: Claude Opus 4.6 (1M context) <noreply@anthropic.com>

nanoclaude/db/database.py

@@ -0,0 +1,47 @@
+"""aiosqlite DB — 요청/응답 로깅 및 메트릭."""
+
+import aiosqlite
+
+from config import settings
+
+SCHEMA = """
+CREATE TABLE IF NOT EXISTS request_logs (
+    id INTEGER PRIMARY KEY AUTOINCREMENT,
+    job_id TEXT NOT NULL,
+    message TEXT NOT NULL,
+    status TEXT NOT NULL DEFAULT 'queued',
+    model TEXT NOT NULL,
+    response_chars INTEGER DEFAULT 0,
+    latency_ms REAL DEFAULT 0,
+    created_at REAL NOT NULL,
+    completed_at REAL
+);
+
+CREATE INDEX IF NOT EXISTS idx_logs_job ON request_logs(job_id);
+CREATE INDEX IF NOT EXISTS idx_logs_created ON request_logs(created_at);
+"""
+
+
+async def init_db():
+    async with aiosqlite.connect(settings.db_path) as db:
+        await db.execute("PRAGMA journal_mode=WAL")
+        await db.executescript(SCHEMA)
+        await db.commit()
+
+
+async def log_request(job_id: str, message: str, model: str, created_at: float):
+    async with aiosqlite.connect(settings.db_path) as db:
+        await db.execute(
+            "INSERT INTO request_logs (job_id, message, model, created_at) VALUES (?, ?, ?, ?)",
+            (job_id, message, model, created_at),
+        )
+        await db.commit()
+
+
+async def log_completion(job_id: str, status: str, response_chars: int, latency_ms: float, completed_at: float):
+    async with aiosqlite.connect(settings.db_path) as db:
+        await db.execute(
+            "UPDATE request_logs SET status=?, response_chars=?, latency_ms=?, completed_at=? WHERE job_id=?",
+            (status, response_chars, latency_ms, completed_at, job_id),
+        )
+        await db.commit()