iOS 13.1.3 has a bug: you can't rearrange app icons! Well, actually you can, but you have to know the trick. Here it is.
The latest iOS version is 13.2, released Monday, October 28th, 2019. If you've already updated to iOS 13, definitely get this update (and keep up with future updates as they come along). This is the first version of iOS 13 that I can recommend. It still has some annoying behaviors but it works well.