The app doesn't trace where you are, or where you have been.
The government can not use it to know whether you have left your house, or where you have been
No data is stored.
All it does is highlight whether you have been close to someone who later self-reports as having symptoms of COVID19 so that you can take appropriate action. It's optional, too. Nobody has to use it who doesn't want to.
As a sneaky way of the government keeping tabs on us, it's a pretty useless design.