Yes, the computer doesn't see the smartphone.
It is connected to the computer via its USB-C cable.
On the old phone a popup-window gave me option to choose to charge battery only or to transfer also files.
Nothing happens on the new phone. Even PupMTP doesn't find it.
However, when I was booting the new smartphone first time and setting everything up,
it detected the WLAN of my Fritz!Box. So, I set it up to be able to use it.
Now, in GoogleDrive app I discovered a revert download button near the video.
So, I thought it must be the upload button.
Then there I found a message with a colored flashing bar: waiting for wlan.
After I switched WLAN to on, on the phone, upload to GoogleDrive started immediately.
A few seconds later I could find it by using my Puppy and GoogleDrive in the web.
It seems GoogleDrive app prefers WLAN connection to upload files.
Don't know why, though.
Since I don't have any limitation on internet and data transfer, I can live with that so far.
Thanks, solved.