fix(core): flaky test completed_commands_do_not_persist_sessions (#3596)

Fix flaky test:
```
        FAIL [   2.641s] codex-core unified_exec::tests::completed_commands_do_not_persist_sessions
  stdout ───

    running 1 test
    test unified_exec::tests::completed_commands_do_not_persist_sessions ... FAILED

    failures:

    failures:
        unified_exec::tests::completed_commands_do_not_persist_sessions

    test result: FAILED. 0 passed; 1 failed; 0 ignored; 0 measured; 235 filtered out; finished in 2.63s
    
  stderr ───

    thread 'unified_exec::tests::completed_commands_do_not_persist_sessions' panicked at core/src/unified_exec/mod.rs:582:9:
    assertion failed: result.output.contains("codex")
```

codex-rs/core/src/unified_exec/mod.rs

@@ -327,6 +327,7 @@ async fn create_unified_exec_session(
 
     let (writer_tx, mut writer_rx) = mpsc::channel::<Vec<u8>>(128);
     let (output_tx, _) = tokio::sync::broadcast::channel::<Vec<u8>>(256);
+    let initial_output_rx = output_tx.subscribe();
 
     let mut reader = pair
         .master
@@ -380,7 +381,7 @@ async fn create_unified_exec_session(
         wait_exit_status.store(true, Ordering::SeqCst);
     });
 
-    Ok(ExecCommandSession::new(
+    let session = ExecCommandSession::new(
         writer_tx,
         output_tx,
         killer,
@@ -388,7 +389,10 @@ async fn create_unified_exec_session(
         writer_handle,
         wait_handle,
         exit_status,
-    ))
+    );
+    session.set_initial_output_receiver(initial_output_rx);
+
+    Ok(session)
 }
 
 #[cfg(test)]