refactor: update api_router initialization to use APIRouter for improved route handling

backend/app/api/router.py

@@ -1,8 +1,10 @@
 """API router aggregation."""
 
+from fastapi import APIRouter
+
 from app.api.routes.v1 import v1_router
 
-# Direct alias — avoids FastAPI 0.135+ validation that rejects routes with
-# empty raw paths (e.g. @router.get("")) when include_router has no prefix.
-# The prefix (settings.API_V1_STR) is applied in main.py.
-api_router = v1_router
+api_router = APIRouter()
+
+# API v1 routes (prefix is set in main.py via settings.API_V1_STR)
+api_router.include_router(v1_router)