After Apple and Google had already created the corresponding interfaces in the smartphone operating system in a joint project to enable Corona Apps, the German version is now on the way.
On the official website you can see how the app works and that it will be available for download from mid-June. After a lot of back and forth, it has fortunately been agreed that personal information will be stored locally (the corresponding data will not leave the phone).
To answer the question of trustworthiness, the app has been designed as an open source project, which means that the source code is freely available to everyone. So if you want to take a look at it or even help developing it, you can find the Corona-Warning app here on GitHub (here the documentation).
How the app works in practice you have to wait and see. The resulting data has to be useful and the battery life shouldn’t suffer too much due to the constant Bluetooth comparison with other smartphones. In addition, it depends on the acceptance of the population: without wide distribution the concept does not work. Therefore, it is a good step to reveal the program code in order to let some professionals evaluate the project, which is technically managed by SAP and Telekom, objectively.