This is an additional development to my above-stated problem. When I connected my MacBookPro 13" to my iPad Pro 12.9" with a lightening cable, my internet connection did not get cut off this time. Previously, I wasn't able to manage that, maybe I did something wrong then, I really don't know.
Now going one step further, I tried to link my mouse and keyboard with a second lightening cable to iPad Pro 9.7" at the same time I was mirroring to iPad Pro 12.9" (again with cable) which I used to do all the time without any cables, just via Wifi before this update. This time, it didn't work with 2 cables, I lost my internet connection again!
I'm waiting for an update fixing this internet problem now.