fix(ai): capture usage and output of incomplete Responses streams

[breken-ai]

💡 Motivation and Context

A Responses API stream that is cut short, for example by max_output_tokens, ends on response.incomplete instead of response.completed. _ResponsesStreamState already reads the stop reason from any terminal event (#919), but extract_openai_usage_from_chunk and extract_openai_content_from_chunk only read response.completed.

As a result, these generations are captured with $ai_stop_reason: max_output_tokens but with no $ai_input_tokens/$ai_output_tokens and an empty $ai_output_choices, even though the tokens were billed and the partial output was streamed. Cost for truncated runs is missing from LLM analytics.

posthog-js's OpenAIResponsesStreamAccumulator takes usage and output from every terminal response. This PR does the same: usage and output are read from response.completed, response.incomplete and response.failed. A stream ends with exactly one of these, so nothing is counted twice.

💚 How did you test it?

• New test test_streaming_responses_api_captures_usage_and_output_when_incomplete streams a real ResponseIncompleteEvent (status incomplete, incomplete_details.reason = max_output_tokens, usage 20/16, a partial output message) through the wrapped OpenAI client.
  • On main (4a138e6) it fails: KeyError: '$ai_input_tokens'.
  • With the fix it passes, including the partial output text.
• pytest posthog 4144 passed, 16 skipped. ruff format --check, ruff check, mypy through mypy-baseline filter and python -W error -c "import posthog" are clean.

📝 Checklist

• I reviewed the submitted code.
• I added tests to verify the changes.
• I updated the docs if needed.
• No breaking change or entry added to the changelog.

If releasing new changes

• Ran sampo add to generate a changeset file

🤖 Agent context

Autonomy: Fully autonomous

• Found and fixed by an autonomous agent (Claude Code, Claude Opus) by comparing the Python OpenAI stream state with posthog-js's Responses accumulator. The failing test was run against main before the fix.
• response.failed is included for parity with posthog-js and with the stop-reason handling. A failed response usually has no usage, and that case is already handled.

Commits here are unsigned; this repo squash-merges, so GitHub signs the merged commit.