fix(app-server): emit turn/started only when turn actually starts (#13261)

This is a follow-up for https://github.com/openai/codex/pull/13047

## Why
We had a race where `turn/started` could be observed before the thread
had actually transitioned to `Active`. This was because we eagerly
emitted `turn/started` in the request handler for `turn/start` (and
`review/start`).

That was showing up as flaky `thread/resume` tests, but the real issue
was broader: a client could see `turn/started` and still get back an
idle thread immediately afterward.

The first idea was to eagerly call
`thread_watch_manager.note_turn_started(...)` from the `turn/start`
request path. That turns out to be unsafe, because
`submit(Op::UserInput)` only queues work. If a turn starts and completes
quickly, request-path bookkeeping can race with the real lifecycle
events and leave stale running state behind.

**The real fix** is to move `turn/started` to emit only after the turn
_actually_ starts, so we do that by waiting for the
`EventMsg::TurnStarted` notification emitted by codex core. We do this
for both `turn/start` and `review/start`.

I also verified this change is safe for our first-party codex apps -
they don't have any assumptions that `turn/started` is emitted before
the RPC response to `turn/start` (which is correct anyway).

I also removed `single_client_mode` since it isn't really necessary now.

## Testing
- `cargo test -p codex-app-server thread_resume -- --nocapture`
- `cargo test -p codex-app-server
'suite::v2::turn_start::turn_start_emits_notifications_and_accepts_model_override'
-- --exact --nocapture`
- `cargo test -p codex-app-server`

codex-rs/app-server/tests/suite/v2/turn_start.rs

@@ -434,6 +434,21 @@ async fn turn_start_emits_notifications_and_accepts_model_override() -> Result<(
         started.turn.status,
         codex_app_server_protocol::TurnStatus::InProgress
     );
+    assert_eq!(started.turn.id, turn.id);
+
+    let completed_notif: JSONRPCNotification = timeout(
+        DEFAULT_READ_TIMEOUT,
+        mcp.read_stream_until_notification_message("turn/completed"),
+    )
+    .await??;
+    let completed: TurnCompletedNotification = serde_json::from_value(
+        completed_notif
+            .params
+            .expect("turn/completed params must be present"),
+    )?;
+    assert_eq!(completed.thread_id, thread.id);
+    assert_eq!(completed.turn.id, turn.id);
+    assert_eq!(completed.turn.status, TurnStatus::Completed);
 
     // Send a second turn that exercises the overrides path: change the model.
     let turn_req2 = mcp
@@ -457,25 +472,30 @@ async fn turn_start_emits_notifications_and_accepts_model_override() -> Result<(
     // Ensure the second turn has a different id than the first.
     assert_ne!(turn.id, turn2.id);
 
-    // Expect a second turn/started notification as well.
-    let _notif2: JSONRPCNotification = timeout(
+    let notif2: JSONRPCNotification = timeout(
         DEFAULT_READ_TIMEOUT,
         mcp.read_stream_until_notification_message("turn/started"),
     )
     .await??;
+    let started2: TurnStartedNotification =
+        serde_json::from_value(notif2.params.expect("params must be present"))?;
+    assert_eq!(started2.thread_id, thread.id);
+    assert_eq!(started2.turn.id, turn2.id);
+    assert_eq!(started2.turn.status, TurnStatus::InProgress);
 
-    let completed_notif: JSONRPCNotification = timeout(
+    let completed_notif2: JSONRPCNotification = timeout(
         DEFAULT_READ_TIMEOUT,
         mcp.read_stream_until_notification_message("turn/completed"),
     )
     .await??;
-    let completed: TurnCompletedNotification = serde_json::from_value(
-        completed_notif
+    let completed2: TurnCompletedNotification = serde_json::from_value(
+        completed_notif2
             .params
             .expect("turn/completed params must be present"),
     )?;
-    assert_eq!(completed.thread_id, thread.id);
-    assert_eq!(completed.turn.status, TurnStatus::Completed);
+    assert_eq!(completed2.thread_id, thread.id);
+    assert_eq!(completed2.turn.id, turn2.id);
+    assert_eq!(completed2.turn.status, TurnStatus::Completed);
 
     Ok(())
 }