Is it possible to force rendering TextArea?

I am using ChatGPT streaming API, which I would like to print to a TextArea. Using the standard print method, it looks like this:

chat_translation_stream = self.client.chat.completions.create(
            ...,
            stream=True
        )
        reply = ""
        for chunk in chat_translation_stream:
            delta = chunk.choices[0].delta.content or ""
            reply += delta
            print(delta, end="", flush=True)

I replaced the print method with something like this in the accept_handler: output_field.buffer.document = Document( text=reply, cursor_position=len(reply) )
But it looks like the the TextArea is only at the end of the handler and not each time the document is modified. Is there a way to force the re-rendering?

Start with the accept_handler and the streaming loop shown in the issue, focusing on how output_field.buffer.document is updated while TextArea is rendered. Trace the prompt-toolkit refresh path and determine what is needed for each streamed delta to become visible; done means the TextArea updates incrementally rather than only after the handler finishes.