I found my mistake eventually.My mistake was explicitly importing
import 'package:sentry/browser_client.dart';
instead of
import 'package:sentry/sentry.dart';
If you needed to use both in this or other cases, you can import it like this:
import 'package:sentry/sentry.dart' if (dart.library.html) 'package:sentry/browser_client.dart' as sentry;