The Nuki App does work on iOS13 when the App is already installed before you update the OS. You will get stuck on some screens but can basically use it.
A fresh install on an iOS13 device does not work because of several changes that Apple made to the rights management system (BLE access, Location access).
We - like Apple - highly recommend to NOT install the iOS13 beta on a production device for the time beeing. Once we have an update to the Nuki App which restores iOS13 compatibility we will make it available in our beta channel.