Anthropic streaming on Python: accumulate text_delta per block, serve via FastAPI StreamingResponse or a Flask generator

# Streaming Claude output from Python (FastAPI and Flask)

1. Start the stream with the SDK's streaming interface, e.g. `client.messages.stream(...)` as a context manager. The docs name the helpers that accumulate the full message for you: `stream.get_final_message()` in Python and `.finalMessage()` in TypeScript.
2. Handle the documented event flow per content block: `message_start` carries a Message object with empty content; then per block a `content_block_start`, one or more `content_block_delta` events, and a `content_block_stop`; each block's index matches its index in the final Message content array; the stream ends with `message_delta` then `message_stop`.
3. Accumulate `text_delta` text per block index. Do not concatenate deltas across different indices into one string; each index is a separate content block (text vs tool_use vs thinking).
4. Ignore unknown event types gracefully. Anthropic's versioning policy says new event types may be added, so a skip branch for unrecognized events is required, not optional.
5. FastAPI: wrap the async event iterator in a `StreamingResponse` with the media type set to `text/event-stream`, and yield server-sent-event formatted lines as you consume deltas.
6. Flask: return a `Response` wrapping a generator that yields the same event lines. Flask's sync view pairs with the SDK's sync streaming interface.
7. Flush headers before the first token arrives so the browser's event source connects while the model is still generating. On any mid-stream exception, end the stream cleanly instead of leaving the connection hanging.

Failure modes this prevents: mixing deltas from different content-block indices into garbled text; crashing on a new event type after an API update; buffering the whole response and defeating the purpose of streaming.