I solved the problem. I erased the iPad again. When I went to installed the beta profile, I realized that before I may have installed the wrong profile (iOS instead of iPadOS).
In both cases, the device was already in iPadOS beta 3. However, the second time, after I installed the right profile I was offered to download an update. I accepted and after that I was able to enable developer mode.
Topic:
Developer Tools & Services
SubTopic:
Xcode
Tags: