Expose environment status through app-server (#32920)

## What changed

- Add the experimental `environment/status` request for inspecting a configured environment without starting or reconnecting it.
- Report `ready`, `pending`, `disconnected`, or `unknown`, including error details for disconnected and unknown environments.
- Probe ready remote environments over their existing exec-server connection.

## Testing

- Add an app-server integration test covering local and remote ready, pending, disconnected, and unknown environments.

GitOrigin-RevId: 397bba603aa9e0b59008ee6cb7cbde46e357652c

codex-rs/app-server/src/request_processors/environment_processor.rs

@@ -52,4 +52,27 @@ impl EnvironmentRequestProcessor {
             .into(),
         ))
     }
+
+    pub(crate) async fn environment_status(
+        &self,
+        params: EnvironmentStatusParams,
+    ) -> Result<Option<ClientResponsePayload>, JSONRPCErrorError> {
+        let environment_id = params.environment_id;
+        let (status, error) = match self
+            .environment_manager
+            .get_environment_status(&environment_id)
+            .await
+        {
+            Some(EnvironmentObservedStatus::Ready) => (EnvironmentStatusKind::Ready, None),
+            Some(EnvironmentObservedStatus::Pending) => (EnvironmentStatusKind::Pending, None),
+            Some(EnvironmentObservedStatus::Disconnected { error }) => {
+                (EnvironmentStatusKind::Disconnected, Some(error))
+            }
+            None => (
+                EnvironmentStatusKind::Unknown,
+                Some(format!("unknown environment id `{environment_id}`")),
+            ),
+        };
+        Ok(Some(EnvironmentStatusResponse { status, error }.into()))
+    }
 }