Advanced data protection cannot be activated

I am using an iPhone Pro 11 with iOS 16.3. I am also using an iPad 11 Pro with the same iOS version.

Account recovery is activated and a recovery has been created.

First problem. Recovery key is shown as "off". That is definitely wrong. See these screenshots:

The main issue is this: I am unable to activate advanced data protection. I have tried it on both devices. I get the following error message:

Any idea what else I could try?