Stabilize app-server notify initialize test (#13939)

## What changed
- This PR changes only the flaky test setup for
`turn_start_notify_payload_includes_initialize_client_name`.
- Instead of shelling out to `python3` to write the notify payload, the
test uses the first-party `codex-app-server-test-notify-capture` helper.
- The helper writes `notify.json` atomically and the test waits for the
file to exist before reading it.

## Why this fixes the flake
- The old test depended on an external Python interpreter being present
and behaving consistently on every CI runner.
- It also raced the file write: the test could observe the path before
the payload had been fully written, which produced partial reads and
intermittent assertion failures.
- Moving the write into a repo-owned helper removes the external
dependency, and atomic write-plus-wait makes the handoff deterministic.

## Scope
- Test-only change.

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

@@ -0,0 +1,44 @@
+use std::env;
+use std::fs;
+use std::fs::File;
+use std::io::Write;
+use std::path::PathBuf;
+
+use anyhow::Context;
+use anyhow::Result;
+use anyhow::anyhow;
+use anyhow::bail;
+
+fn main() -> Result<()> {
+    let mut args = env::args_os();
+    let _program = args.next();
+    let output_path = PathBuf::from(
+        args.next()
+            .ok_or_else(|| anyhow!("expected output path as first argument"))?,
+    );
+    let payload = args
+        .next()
+        .ok_or_else(|| anyhow!("expected payload as final argument"))?;
+
+    if args.next().is_some() {
+        bail!("expected payload as final argument");
+    }
+
+    let payload = payload.to_string_lossy();
+    let temp_path = PathBuf::from(format!("{}.tmp", output_path.display()));
+    let mut file = File::create(&temp_path)
+        .with_context(|| format!("failed to create {}", temp_path.display()))?;
+    file.write_all(payload.as_bytes())
+        .with_context(|| format!("failed to write {}", temp_path.display()))?;
+    file.sync_all()
+        .with_context(|| format!("failed to sync {}", temp_path.display()))?;
+    fs::rename(&temp_path, &output_path).with_context(|| {
+        format!(
+            "failed to move {} into {}",
+            temp_path.display(),
+            output_path.display()
+        )
+    })?;
+
+    Ok(())
+}