[App-server] v2 for account/updated and account/logout (#6175)

V2 for `account/updated` and `account/logout` for app server. correspond
to old `authStatusChange` and `LogoutChatGpt` respectively. Followup PRs
will make other v2 endpoints call `account/updated` instead of
`authStatusChange` too.

codex-rs/app-server/src/outgoing_message.rs

@@ -141,6 +141,8 @@ pub(crate) struct OutgoingError {
 
 #[cfg(test)]
 mod tests {
+    use codex_app_server_protocol::AccountUpdatedNotification;
+    use codex_app_server_protocol::AuthMode;
     use codex_app_server_protocol::LoginChatGptCompleteNotification;
     use codex_protocol::protocol::RateLimitSnapshot;
     use codex_protocol::protocol::RateLimitWindow;
@@ -204,4 +206,24 @@ mod tests {
             "ensure the notification serializes correctly"
         );
     }
+
+    #[test]
+    fn verify_account_updated_notification_serialization() {
+        let notification = ServerNotification::AccountUpdated(AccountUpdatedNotification {
+            auth_method: Some(AuthMode::ApiKey),
+        });
+
+        let jsonrpc_notification = OutgoingMessage::AppServerNotification(notification);
+        assert_eq!(
+            json!({
+                "method": "account/updated",
+                "params": {
+                    "authMethod": "apikey"
+                },
+            }),
+            serde_json::to_value(jsonrpc_notification)
+                .expect("ensure the notification serializes correctly"),
+            "ensure the notification serializes correctly"
+        );
+    }
 }