iPad got slow, missing drive space
Part of the 16GB is taken up by iOS. The system usage screen won't show a category for the OS itself because there's nothing you can do about it.

Your device is coming up on about five years old. Modern device will perform much better on a more resource intensive OS. You could try a restore but really I think it's just that the new features and technologies aren't well optimized or are simply too much for it.