[DOCS] `Build a streaming UI` miss the the check for in_tool

Documentation Type

Missing documentation (feature not documented)

Documentation Location

https://code.claude.com/docs/en/agent-sdk/streaming-output#build-a-streaming-ui

Section/Topic

build-a-streaming-ui

Current Documentation

The docs current show:

elif event_type == "content_block_delta":
      delta = event.get("delta", {})
      # Only stream text when not executing a tool
      if delta.get("type") == "text_delta" and not in_tool:
          sys.stdout.write(delta.get("text", ""))
          sys.stdout.flush()

What's Wrong or Missing?

The code miss the in_tool case process.

Suggested Improvement

elif event_type == "content_block_delta":
      delta = event.get("delta", {})
      delta_type = delta.get("type")

      if delta_type == "text_delta" and not in_tool:
          # Streaming text from Claude's response
          sys.stdout.write(delta.get("text", ""))
          sys.stdout.flush()

      elif delta_type == "input_json_delta" and in_tool:
          # ✅ Accumulate tool input JSON as it streams in
          tool_input += delta.get("partial_json", "")
elif event_type == "content_block_stop":
    if in_tool:
        # Tool call finished — tool_input now has the complete JSON
        print(f" done (input: {tool_input})", flush=True)
        in_tool = False
        tool_input = ""

Impact

Medium - Makes feature difficult to understand

Additional Context

_No response_