feat: add GET /api/models endpoint

Returns available Claude models from SDK and the configured default model.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

src/backend/api/routes/health.py

@@ -1,8 +1,9 @@
 from fastapi import APIRouter, Depends
 
 from src.backend.api.dependencies import verify_api_key
+from src.backend.config import settings
 from src.backend.db.database import get_db
-from src.backend.models.api import ok
+from src.backend.models.api import ok, fail
 from src.backend.services.worker_client import WorkerClient
 
 router = APIRouter(dependencies=[Depends(verify_api_key)])
@@ -26,3 +27,17 @@ async def health():
         "database": db_ok,
         "worker": worker_ok,
     })
+
+
+@router.get("/models", summary="List available models", tags=["system"])
+async def list_models():
+    worker = WorkerClient()
+    result = await worker.models()
+
+    if not result.get("success"):
+        return fail("WORKER_ERROR", result.get("error", "Failed to fetch models"))
+
+    return ok({
+        "default_model": settings.claude_model,
+        "models": result["models"],
+    })

src/backend/services/worker_client.py

@@ -38,6 +38,11 @@ class WorkerClient:
             )
             return resp.json()
 
+    async def models(self) -> dict:
+        async with httpx.AsyncClient(timeout=30.0) as client:
+            resp = await client.get(f"{self.base_url}/models")
+            return resp.json()
+
     async def health(self) -> bool:
         try:
             async with httpx.AsyncClient(timeout=5.0) as client: