Thank you for your extended answer Mary. My screen looks like yours using camera, but not with video. As you can see on my screenshot, the tick box is missing. None of te other icons do anything useful either. So my camera app behaves different (it's the default app).
I had as only software that I could imagine doing something weird, the Nova Launcher installed. I removed that but the result stays the same. The phone is a Nokia 7 plus with Android One, currently at version 9.