Thanks for the reply! I already did everything like you described but when I open the apk with a file manager (allowing external apk installation for it) and select install, it just doesn't work because it tells me "error" and "cannot open file/folder!".
I retried with a different file manager. First one with the error was the popular total commander.
The second one worked! It is the file manager that was already installed on my phone (Huawei P30 pro).
Thank you for your help! The additional information is very helpful
So maybe the issue is that total commander can't handle that the installation is blocked by play protect but the other file manager named "files" can. The working file manager shows me the following dialog and lets me decide if I want to install the app or not.
Nice that it works now! I will mark the topic as solved.
I also tried using the ADB console and it worked. But I had to do additional steps. So first I needed to activate USB debugging on my phone. After that it got listed and selected automatically in Visual Studio. And since I had an emulator running in parallel the tool refused to install the app. I solved this by listing the devices with the ADB tool and then used the serial number to specify where ADB should install the app. Also since the full path to the signed app had spaces I had to use quotes around the path.