Add multi-agent mode to thread settings updates

[shijie-oai]

Why

Clients can select multi-agent mode through thread/start and turn/start, but they cannot currently change a loaded thread's selection without starting a turn. thread/settings/update already exists for changing sticky next-turn settings independently of model execution, so multi-agent mode should use the same path.

What changed

• Add the optional experimental thread/settings/update.multiAgentMode field with explicitRequestOnly and proactive values.
• Pass the selected mode through the existing thread-settings update pipeline so it becomes the loaded session's selection for subsequent turns.
• Return the updated selection through the existing thread/settings/updated notification without starting a model request or adding transcript items.
• Document the new request field in the app-server API overview.
• Add end-to-end coverage verifying that a proactive settings update is reported immediately and, between two eligible turns, appends exactly one proactive developer update while retaining the prior explicit baseline without duplication.

Omitting multiAgentMode leaves the loaded session's selection unchanged. As with turn/start, this API does not currently provide a distinct operation for clearing an existing selection back to unset.

Verification

• CARGO_INCREMENTAL=0 just test -p codex-app-server-protocol
• CARGO_INCREMENTAL=0 just test -p codex-app-server thread_settings_update
• CARGO_INCREMENTAL=0 just test -p codex-app-server thread_settings_update_multi_agent_mode_applies_to_future_turns
• CARGO_INCREMENTAL=0 just fix -p codex-app-server-protocol -p codex-app-server
• just fmt

Stack

Stacked on #28792, which adds thread-start initialization and lifecycle/settings observability for multi-agent mode. The underlying per-turn mode behavior is introduced in #28685.