Add unfinished root turn suspension (#40038)

## Why

An active root turn needs to be stopped without marking it complete or aborted
before another runtime can recover the same turn ID.

## What changed

- Add `CodexThread::suspend_turn_and_shutdown` and `SuspendTurnOutcome`.
- Flush history, stop the active regular task, close the history writer, and
  shut down the session without recording a terminal turn event.
- Reject suspension when no supported turn is active or the loaded agent
  subtree still contains a live descendant.

## Testing

- Verify that suspension preserves unfinished history and allows the turn to be
  recovered under its original ID after the descendant guard is cleared.

GitOrigin-RevId: 1f9b019d07c51474ec2d991d263bc15cdd4f89ad

codex-rs/protocol/src/protocol.rs

@@ -56,6 +56,7 @@ use crate::plan_tool::UpdatePlanArgs;
 use crate::request_permissions::RequestPermissionsEvent;
 use crate::request_permissions::RequestPermissionsResponse;
 use crate::request_user_input::RequestUserInputResponse;
+use crate::turn_input::SuspendTurnOutcome;
 use crate::turn_input::TurnInputMode;
 use crate::turn_input::TurnInputRequest;
 use crate::turn_input::TurnInputSubmission;
@@ -581,6 +582,11 @@ pub enum Op {
         reply: oneshot::Sender<CodexResult<TurnInputSubmission>>,
     },
 
+    /// Stop the active root turn without recording a terminal turn event.
+    SuspendTurnAndShutdown {
+        reply: oneshot::Sender<CodexResult<SuspendTurnOutcome>>,
+    },
+
     /// Apply persistent thread-settings overrides without starting a turn.
     ///
     /// This uses the same submission queue as turn starts so app-server can
@@ -875,6 +881,7 @@ impl Op {
             Self::RealtimeConversationListVoices => "realtime_conversation_list_voices",
             Self::TurnInput { .. } => "turn_input",
             Self::RecoverTurn { .. } => "recover_turn",
+            Self::SuspendTurnAndShutdown { .. } => "suspend_turn_and_shutdown",
             Self::ThreadSettings { .. } => "thread_settings",
             Self::InterAgentCommunication { .. } => "inter_agent_communication",
             Self::ExecApproval { .. } => "exec_approval",

codex-rs/protocol/src/turn_input.rs

@@ -13,6 +13,18 @@ use serde_json::Value;
 use std::collections::BTreeMap;
 use std::collections::HashMap;
 
+/// Result of stopping an unfinished root turn so another worker can recover it.
+#[derive(Clone, Debug, PartialEq, Eq)]
+pub enum SuspendTurnOutcome {
+    Suspended {
+        turn_id: String,
+    },
+    NotActive,
+    /// A currently loaded descendant would remain running after root handoff.
+    HasLiveDescendants,
+    UnsupportedTask,
+}
+
 /// Input consumed by a regular turn.
 #[derive(Clone, Debug, PartialEq, Serialize, Deserialize)]
 pub enum TurnInput {