Cannot rearrange apps on new iPad Pro - what do I do?

Try pushing on the app with some force.

Also, go to Settings > Screen Time > Content & Privacy Restrictions > iTunes & App Store Purchases > and make sure installing and deleting apps is allowed.

That's correct. In iPadOS 13, the process is different. All you have to do is hold your finger on any app until a box pops up and one option will be Edit Home Screen. Tap that and all the apps will jiggle as they did before.