Stabilize abort task follow-up handling (#13874)

- production logic plus tests; cancel running tasks before clearing
pending turn state
- suppress follow-up model requests after cancellation and assert on
stabilized request counts instead of fixed sleeps

codex-rs/app-server/src/bin/test_notify_capture.rs

@@ -0,0 +1,23 @@
+use anyhow::Result;
+use anyhow::anyhow;
+use std::env;
+use std::path::PathBuf;
+
+fn main() -> Result<()> {
+    let mut args = env::args_os().skip(1);
+    let output_path = PathBuf::from(
+        args.next()
+            .ok_or_else(|| anyhow!("missing output path argument"))?,
+    );
+    let payload = args
+        .next()
+        .ok_or_else(|| anyhow!("missing payload argument"))?
+        .into_string()
+        .map_err(|_| anyhow!("payload must be valid UTF-8"))?;
+
+    let temp_path = output_path.with_extension("json.tmp");
+    std::fs::write(&temp_path, payload)?;
+    std::fs::rename(&temp_path, &output_path)?;
+
+    Ok(())
+}