feat: add gateway module with FastAPI server (#5)

* chore: add .claude/ to .gitignore

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

* feat: add gateway module with FastAPI server

- Add new gateway module with FastAPI app for API routing
- Add gateway and serve commands to Makefile
- Add fastapi, httpx, uvicorn, sse-starlette dependencies
- Fix model config retrieval in lead_agent (support both model_name and model)

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

---------

Co-authored-by: Claude Opus 4.5 <noreply@anthropic.com>

backend/src/gateway/routers/models.py

@@ -0,0 +1,67 @@
+from fastapi import APIRouter, HTTPException
+from pydantic import BaseModel, Field
+
+from src.config import get_app_config
+
+router = APIRouter(prefix="/api", tags=["models"])
+
+
+class ModelResponse(BaseModel):
+    """Response model for model information."""
+
+    name: str = Field(..., description="Unique identifier for the model")
+    display_name: str | None = Field(None, description="Human-readable name")
+    description: str | None = Field(None, description="Model description")
+    supports_thinking: bool = Field(default=False, description="Whether model supports thinking mode")
+
+
+class ModelsListResponse(BaseModel):
+    """Response model for listing all models."""
+
+    models: list[ModelResponse]
+
+
+@router.get("/models", response_model=ModelsListResponse)
+async def list_models() -> ModelsListResponse:
+    """List all available models from configuration.
+
+    Returns model information suitable for frontend display,
+    excluding sensitive fields like API keys and internal configuration.
+    """
+    config = get_app_config()
+    models = [
+        ModelResponse(
+            name=model.name,
+            display_name=model.display_name,
+            description=model.description,
+            supports_thinking=model.supports_thinking,
+        )
+        for model in config.models
+    ]
+    return ModelsListResponse(models=models)
+
+
+@router.get("/models/{model_name}", response_model=ModelResponse)
+async def get_model(model_name: str) -> ModelResponse:
+    """Get a specific model by name.
+
+    Args:
+        model_name: The unique name of the model to retrieve.
+
+    Returns:
+        Model information if found.
+
+    Raises:
+        HTTPException: 404 if model not found.
+    """
+    config = get_app_config()
+    model = config.get_model_config(model_name)
+    if model is None:
+        raise HTTPException(status_code=404, detail=f"Model '{model_name}' not found")
+
+    return ModelResponse(
+        name=model.name,
+        display_name=model.display_name,
+        description=model.description,
+        supports_thinking=model.supports_thinking,
+    )