Log received messages for exceptions as well as timeouts (#23287)

diff --git a/packages/flutter_tools/test/integration/test_driver.dart b/packages/flutter_tools/test/integration/test_driver.dart
index c7d89c7..685dff0 100644
--- a/packages/flutter_tools/test/integration/test_driver.dart
+++ b/packages/flutter_tools/test/integration/test_driver.dart
@@ -372,7 +372,9 @@
 
     return f().timeout(timeout ?? defaultTimeout, onTimeout: () {
       logMessage('<timed out>');
-      throw '$message\nReceived:\n${messages.toString()}';
+      throw '$message';
+    }).catchError((dynamic error) {
+      throw '$error\nReceived:\n${messages.toString()}';
     }).whenComplete(() => sub.cancel());
   }