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/main.py

@@ -0,0 +1,46 @@
+from contextlib import asynccontextmanager
+
+from fastapi import FastAPI
+from fastapi.middleware.cors import CORSMiddleware
+
+from config import settings
+from middleware.auth import AuthMiddleware
+from routers import auth, chat, embeddings, gpu, health, models
+from services.registry import registry
+
+
+@asynccontextmanager
+async def lifespan(app: FastAPI):
+    await registry.load_backends(settings.backends_config)
+    registry.start_health_loop()
+    yield
+    registry.stop_health_loop()
+
+
+app = FastAPI(
+    title="AI Gateway",
+    version="0.1.0",
+    lifespan=lifespan,
+)
+
+app.add_middleware(
+    CORSMiddleware,
+    allow_origins=settings.cors_origins.split(","),
+    allow_credentials=True,
+    allow_methods=["*"],
+    allow_headers=["*"],
+)
+
+app.add_middleware(AuthMiddleware)
+
+app.include_router(auth.router)
+app.include_router(chat.router)
+app.include_router(models.router)
+app.include_router(embeddings.router)
+app.include_router(health.router)
+app.include_router(gpu.router)
+
+
+@app.get("/")
+async def root():
+    return {"service": "AI Gateway", "version": "0.1.0"}