docs: expand multi-prompt context carry-over details

[Zireaeler]

Motivation

• Clarify how multi-call turns carry prior prompt context into subsequent model requests with concrete, repo-local detail.
• Respond to inline feedback by adding an explicit subsection that explains where carry-over is stored, how history is rebuilt, and how function calls and outputs are appended.

Description

• Add docs/codex-request-lifecycle.md updates: new section 3.1 that states carry-over lives in ResponsesApiRequest.input and is encoded as Vec<ResponseItem> with structured items (message, function_call, function_call_output).
• Describe the per-round pipeline (OutputItemDone → record function_call → execute tool → record function_call_output → rebuild sampling_request_input) and emphasize that history is replayed structurally rather than by copying assistant plaintext.
• Include concrete JSON examples for Call docs: expand multi-prompt context carry-over details #1 / Call Codex-generated pull request #2 / Call move all tests under tests/ openai/codex#3 showing appended function_call and function_call_output items, and summarize which request fields typically remain stable (instructions, tool_choice, stream, prompt_cache_key) versus which change (input, tools, reasoning/include/text).
• Explain compaction behavior: when tokens near limit the next input can become a summary + recent critical items instead of the full raw history.

Testing

• No automated tests were run because this is a documentation-only change.
• No runtime or Rust code was modified, so no cargo test or workspace formatting was required for this PR.

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Codex Task