[6/6] Fail exec client operations after disconnect (#18027)

## Summary
- Reject new exec-server client operations once the transport has
disconnected.
- Convert pending RPC calls into closed errors instead of synthetic
server errors.
- Cover pending read and later write behavior after remote executor
disconnect.

## Verification
- `just fmt`
- `cargo check -p codex-exec-server`

## Stack
```text
@  #18027 [6/6] Fail exec client operations after disconnect
│
o  #18212 [5/6] Wire executor-backed MCP stdio
│
o  #18087 [4/6] Abstract MCP stdio server launching
│
o  #18020 [3/6] Add pushed exec process events
│
o  #18086 [2/6] Support piped stdin in exec process API
│
o  #18085 [1/6] Add MCP server environment config
│
o  main
```

---------

Co-authored-by: Codex <noreply@openai.com>

codex-rs/exec-server/src/remote_file_system.rs

@@ -195,9 +195,46 @@ fn map_remote_error(error: ExecServerError) -> io::Error {
             io::Error::new(io::ErrorKind::InvalidInput, message)
         }
         ExecServerError::Server { message, .. } => io::Error::other(message),
-        ExecServerError::Closed => {
+        ExecServerError::Closed | ExecServerError::Disconnected(_) => {
             io::Error::new(io::ErrorKind::BrokenPipe, "exec-server transport closed")
         }
         _ => io::Error::other(error.to_string()),
     }
 }
+
+#[cfg(test)]
+mod tests {
+    use pretty_assertions::assert_eq;
+
+    use super::*;
+
+    #[test]
+    fn transport_errors_map_to_broken_pipe() {
+        let errors = [
+            ExecServerError::Closed,
+            ExecServerError::Disconnected("exec-server transport disconnected".to_string()),
+        ];
+
+        let mapped_errors = errors
+            .into_iter()
+            .map(|error| {
+                let error = map_remote_error(error);
+                (error.kind(), error.to_string())
+            })
+            .collect::<Vec<_>>();
+
+        assert_eq!(
+            mapped_errors,
+            vec![
+                (
+                    io::ErrorKind::BrokenPipe,
+                    "exec-server transport closed".to_string()
+                ),
+                (
+                    io::ErrorKind::BrokenPipe,
+                    "exec-server transport closed".to_string()
+                ),
+            ]
+        );
+    }
+}