Currently we're using flutter drive to run integration tests, which logs:

flutter: Warning: integration_test plugin was not detected.
flutter:
flutter: If you're running the tests with `flutter drive`, please make sure your tests
flutter: are in the `integration_test/` directory of your package and use
flutter: `flutter test $path_to_test` to run it instead.

For the non-web platforms, we should switch from flutter drive to flutter test integration_test. (We'll likely need to resolve the TODO about the one remaining old-style driver test structure we have in video_player, since flutter test expects all tests to be in integration_test)