feat: AI Gateway Phase 1 - FastAPI 코어 구현

GPU 서버 중앙 AI 라우팅 서비스 초기 구현:
- OpenAI 호환 API (/v1/chat/completions, /v1/models, /v1/embeddings)
- 모델 레지스트리 + 백엔드 헬스체크 (30초 루프)
- Ollama SSE 프록시 (NDJSON → OpenAI SSE 변환)
- JWT 인증 이중 경로 (httpOnly 쿠키 + Bearer 토큰)
- owner/guest 역할 분리, 로그인 rate limiting
- 백엔드별 rate limiting (NanoClaude 대비)
- SQLite 스키마 사전 정의 (aiosqlite + WAL)
- Docker Compose + Caddy 리버스 프록시

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

hub-api/db/database.py

@@ -0,0 +1,50 @@
+import aiosqlite
+
+from config import settings
+
+SCHEMA = """
+CREATE TABLE IF NOT EXISTS chat_sessions (
+    id TEXT PRIMARY KEY,
+    title TEXT,
+    model TEXT NOT NULL,
+    role TEXT NOT NULL DEFAULT 'guest',
+    created_at REAL NOT NULL
+);
+
+CREATE TABLE IF NOT EXISTS chat_messages (
+    id TEXT PRIMARY KEY,
+    session_id TEXT NOT NULL REFERENCES chat_sessions(id),
+    role TEXT NOT NULL,
+    content TEXT NOT NULL,
+    created_at REAL NOT NULL
+);
+
+CREATE TABLE IF NOT EXISTS usage_logs (
+    id INTEGER PRIMARY KEY AUTOINCREMENT,
+    backend_id TEXT NOT NULL,
+    model TEXT NOT NULL,
+    prompt_tokens INTEGER DEFAULT 0,
+    completion_tokens INTEGER DEFAULT 0,
+    latency_ms REAL DEFAULT 0,
+    user_role TEXT NOT NULL DEFAULT 'guest',
+    created_at REAL NOT NULL
+);
+
+CREATE INDEX IF NOT EXISTS idx_messages_session ON chat_messages(session_id);
+CREATE INDEX IF NOT EXISTS idx_usage_created ON usage_logs(created_at);
+"""
+
+
+async def init_db():
+    """Initialize SQLite database with WAL mode and schema."""
+    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 get_db() -> aiosqlite.Connection:
+    """Get a database connection."""
+    db = await aiosqlite.connect(settings.db_path)
+    await db.execute("PRAGMA journal_mode=WAL")
+    return db