The German Corona-Warn-App is unique because
- the code is open source,
- there is no obligation to install it, and
- central data processing is limited to what is necessary to inform people who might have been in contact with an infected person; only the Temporary Exposure Keys are send from the phone to the server in case a person identifies himself/herself as being infected.
I think no other government in the world has this open and voluntary approach. To support the experiment, and of course if there is a chance the app would help to trace infection chains, I believe it´s worth to install it. Unfortunately, my phone is six years old and doesn´t support the version of iOS necessary to run the app. I´m on iOS 12.4.7 and at least you need 13.5.
I´ve heard such an app would only make sense if 60% of our population use it. That´s difficult. The only app with such a widespread use in Germany is WhatsApp. But let´s see how it goes. I think it´s worth installing.