[codex] control automatic realtime handoff delivery

[jiayuhuang-openai]

What

Built on the realtime speech-control plumbing merged in #27917.

• Add optional codexResponseHandoffPrefix to thread/realtime/start.
• Apply that prefix only to automatic V1 commentary sent through conversation.handoff.append; final answers remain unprefixed.
• Add opt-in clientManagedHandoffs. When true, core suppresses automatic response handoffs and completion output so delivery is controlled by explicit client append APIs.
• Preserve existing automatic behavior by default. codexResponsesAsItems: true continues to select item routing when client-managed mode is disabled.

Why

Voice clients need two delivery policies: automatic background context with silent commentary instructions and fully client-owned handoffs. Phase-aware prefixing keeps routine commentary silent without suppressing the final answer, while client-managed mode lets an app decide exactly which updates to append.

Validation

• just fmt
• cargo test -p codex-app-server-protocol serialize_thread_realtime_start
• RUST_MIN_STACK=16777216 cargo test -p codex-core --test all conversation_handoff_persists_across_item_done_until_turn_complete
• RUST_MIN_STACK=16777216 cargo test -p codex-app-server --test all webrtc_v1_client_managed_handoffs_disable_automatic_output
• RUST_MIN_STACK=16777216 cargo test -p codex-app-server --test all webrtc_v1_final_automatic_handoff_omits_silent_prefix
• cargo build -p codex-cli --bin codex
• Local Codex Apps compatibility check: 43 focused webview tests passed, and a live voice session routed through the source-built app-server.

The explicit RUST_MIN_STACK avoids a macOS Tokio test-worker stack overflow seen with the default test environment.

[github-actions]

All contributors have signed the CLA ✍️ ✅
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[guinness-oai]

why do we need a new outbound type here?

[chatgpt-codex-connector]

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[chatgpt-codex-connector]

Preserve default routing for empty handoff prefixes

When a client sends codexResponseHandoffPrefix: "" for a V1 active handoff, this is_some() check takes the new direct HandoffAppend path even though realtime_backend_item treats the empty prefix as absent. That bypasses the existing send_conversation_function_call_output path, so the response loses the default "Agent Final Message" wrapper that omission/null still gets; clients that bind an empty text input instead of omitting the field will silently change realtime behavior. Consider checking for a non-empty prefix before switching paths.

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[jiayuhuang-openai]

I have read the CLA Document and I hereby sign the CLA

[jiayuhuang-openai]

/merge