I tried your suggestion (going to "Movies" and "TV-programs" once I've entered "Content restrictions) and set both to "Don't allow" but it made no difference with the TV app.
The "Watch now" is still there and still has stuff on the front page which isn't suitable for children. There must be a way to do away with that.
Is there a way I can completely block the TV app then, so the Screen time passcode is the only way to open it?
(I know there's an "Accept apps" section within the screen time "Content and privacy" section, but it only shows a few apps, and TV isn't one of them.