Hello again,
UBports installer worked. There is an option where you can activate ADB mode when you start the phone, somewhere in the boot menu. With this, my phone was recognized automatically by the UBports because this activates something like developer mode.
In case someone reads this: it would be great if the UBports-installer would provide clearer information when to connect the phone with the PC.
In any case, you can mark this thread as solved, thank you very much, your support is much appreciated.