[Feature] Add basic metrics for /realtime endpoint (#35500)

Signed-off-by: Thomas Pouget-Abadie <thomaspou@microsoft.com>
Signed-off-by: pougetat <thomas.pougetabadie@gmail.com>
Co-authored-by: Thomas Pouget-Abadie <thomaspou@microsoft.com>
Co-authored-by: gemini-code-assist[bot] <176961590+gemini-code-assist[bot]@users.noreply.github.com>

vllm/entrypoints/openai/api_server.py

@@ -264,6 +264,14 @@ def build_app(
     # Add scaling middleware to check for scaling state
     app.add_middleware(ScalingMiddleware)
 
+    if "realtime" in supported_tasks:
+        # Add WebSocket metrics middleware
+        from vllm.entrypoints.openai.realtime.metrics import (
+            WebSocketMetricsMiddleware,
+        )
+
+        app.add_middleware(WebSocketMetricsMiddleware)
+
     if envs.VLLM_DEBUG_LOG_API_SERVER_RESPONSE:
         logger.warning(
             "CAUTION: Enabling log response in the API Server. "