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/routers/chat.py

@@ -0,0 +1,92 @@
+from typing import List, Optional
+
+from fastapi import APIRouter, HTTPException, Request
+from fastapi.responses import JSONResponse, StreamingResponse
+from pydantic import BaseModel
+
+from middleware.rate_limit import check_backend_rate_limit
+from services import proxy_ollama
+from services.registry import registry
+
+router = APIRouter(prefix="/v1", tags=["chat"])
+
+
+class ChatMessage(BaseModel):
+    role: str
+    content: str
+
+
+class ChatRequest(BaseModel):
+    model: str
+    messages: List[ChatMessage]
+    stream: bool = False
+    temperature: Optional[float] = None
+    max_tokens: Optional[int] = None
+
+
+@router.post("/chat/completions")
+async def chat_completions(body: ChatRequest, request: Request):
+    role = getattr(request.state, "role", "anonymous")
+    if role == "anonymous":
+        raise HTTPException(
+            status_code=401,
+            detail={"error": {"message": "Authentication required", "type": "auth_error", "code": "unauthorized"}},
+        )
+
+    # Resolve model to backend
+    result = registry.resolve_model(body.model, role)
+    if not result:
+        raise HTTPException(
+            status_code=404,
+            detail={
+                "error": {
+                    "message": f"Model '{body.model}' not found or not available",
+                    "type": "invalid_request_error",
+                    "code": "model_not_found",
+                }
+            },
+        )
+
+    backend, model_info = result
+
+    # Check rate limit
+    check_backend_rate_limit(backend.id)
+
+    # Record request for rate limiting
+    registry.record_request(backend.id)
+
+    messages = [{"role": m.role, "content": m.content} for m in body.messages]
+    kwargs = {}
+    if body.temperature is not None:
+        kwargs["temperature"] = body.temperature
+
+    # Route to appropriate proxy
+    if backend.type == "ollama":
+        if body.stream:
+            return StreamingResponse(
+                proxy_ollama.stream_chat(
+                    backend.url, body.model, messages, **kwargs
+                ),
+                media_type="text/event-stream",
+                headers={
+                    "Cache-Control": "no-cache",
+                    "X-Accel-Buffering": "no",
+                },
+            )
+        else:
+            result = await proxy_ollama.complete_chat(
+                backend.url, body.model, messages, **kwargs
+            )
+            return JSONResponse(content=result)
+
+    # Placeholder for other backend types
+    raise HTTPException(
+        status_code=501,
+        detail={
+            "error": {
+                "message": f"Backend type '{backend.type}' not yet implemented",
+                "type": "api_error",
+                "code": "not_implemented",
+            }
+        },
+    )