fix: save streaming input to session before outputs

[seratch]

Summary

• persist the streamed run input in the session before outputs so the transcript order is correct

Testing

• pnpm -r build-check (fails: @openai/agents-openai build-check: tsc --noEmit -p ./tsconfig.test.json)

---

https://chatgpt.com/codex/tasks/task_i_68b7c67600cc832094220231a8aade48

[changeset-bot]

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Latest commit: 49675a7

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