[BugFix] anthropic/serving_messages: fix tool call arguments streaming (#34887)

Signed-off-by: Daniele Trifirò <dtrifiro@redhat.com>
Co-authored-by: Nicolò Lucchesi <nlucches@redhat.com>

vllm/entrypoints/anthropic/serving.py

@@ -432,6 +432,19 @@ class AnthropicServingMessages(OpenAIServingChat):
                                 data = chunk.model_dump_json(exclude_unset=True)
                                 yield wrap_data_with_event(data, "content_block_start")
                                 content_block_started = True
+                                if tool_call.function and tool_call.function.arguments:
+                                    chunk = AnthropicStreamEvent(
+                                        index=content_block_index,
+                                        type="content_block_delta",
+                                        delta=AnthropicDelta(
+                                            type="input_json_delta",
+                                            partial_json=tool_call.function.arguments,
+                                        ),
+                                    )
+                                    data = chunk.model_dump_json(exclude_unset=True)
+                                    yield wrap_data_with_event(
+                                        data, "content_block_delta"
+                                    )
 
                             else:
                                 chunk = AnthropicStreamEvent(