[MCP] Fix vestigial token yield on early exit (#3132)

* Don't yield tokens on early exit

* Apply style fixes

---------

Co-authored-by: github-actions[bot] <github-actions[bot]@users.noreply.github.com>
Co-authored-by: Lucain <[email protected]>

Author: 3 people

src/huggingface_hub/inference/_mcp/mcp_client.py

@@ -272,9 +272,6 @@ async def process_single_turn_with_tools(
 
         # Read from stream
         async for chunk in response:
-            # Yield each chunk to caller
-            yield chunk
-
             num_of_chunks += 1
             delta = chunk.choices[0].delta if chunk.choices and len(chunk.choices) > 0 else None
             if not delta:
@@ -304,6 +301,9 @@ async def process_single_turn_with_tools(
             if exit_if_first_chunk_no_tool and num_of_chunks <= 2 and len(final_tool_calls) == 0:
                 return
 
+            # Yield each chunk to caller
+            yield chunk
+
         if message["content"]:
             messages.append(message)