[Bugfix][Frontend] Fix missing /metrics endpoint (#6463)

vllm/entrypoints/openai/api_server.py

@@ -73,11 +73,13 @@ async def lifespan(app: fastapi.FastAPI):
 
 router = APIRouter()
 
-# Add prometheus asgi middleware to route /metrics requests
-route = Mount("/metrics", make_asgi_app())
-# Workaround for 307 Redirect for /metrics
-route.path_regex = re.compile('^/metrics(?P<path>.*)$')
-router.routes.append(route)
+
+def mount_metrics(app: fastapi.FastAPI):
+    # Add prometheus asgi middleware to route /metrics requests
+    metrics_route = Mount("/metrics", make_asgi_app())
+    # Workaround for 307 Redirect for /metrics
+    metrics_route.path_regex = re.compile('^/metrics(?P<path>.*)$')
+    app.routes.append(metrics_route)
 
 
 @router.get("/health")
@@ -167,6 +169,8 @@ def build_app(args):
     app.include_router(router)
     app.root_path = args.root_path
 
+    mount_metrics(app)
+
     app.add_middleware(
         CORSMiddleware,
         allow_origins=args.allowed_origins,