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/embeddings.py

@@ -0,0 +1,67 @@
+from typing import List, Union
+
+from fastapi import APIRouter, HTTPException, Request
+from pydantic import BaseModel
+
+from services import proxy_ollama
+from services.registry import registry
+
+router = APIRouter(prefix="/v1", tags=["embeddings"])
+
+
+class EmbeddingRequest(BaseModel):
+    model: str
+    input: Union[str, List[str]]
+
+
+@router.post("/embeddings")
+async def create_embedding(body: EmbeddingRequest, 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"}},
+        )
+
+    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
+
+    if "embed" not in model_info.capabilities:
+        raise HTTPException(
+            status_code=400,
+            detail={
+                "error": {
+                    "message": f"Model '{body.model}' does not support embeddings",
+                    "type": "invalid_request_error",
+                    "code": "capability_mismatch",
+                }
+            },
+        )
+
+    if backend.type == "ollama":
+        return await proxy_ollama.generate_embedding(
+            backend.url, body.model, body.input
+        )
+
+    raise HTTPException(
+        status_code=501,
+        detail={
+            "error": {
+                "message": f"Embedding not supported for backend type '{backend.type}'",
+                "type": "api_error",
+                "code": "not_implemented",
+            }
+        },
+    )