Since I am using the iPhone X I noticed that the search in the settings didn't work anymore. I guess it was working until I restored the latest backup from iCloud when I was setting up the device. I am also using the Beta versions of iOS 11 for quite a long time so that would have been also the reason for it.
Whatever it caused, it was annoying (some other issues still exist though...). Now I found the solution for this problem (sorry, the screenshots are in German):
Open the settings and scroll to "Search & Siri" to open it:
After you opened it scroll down to the list of apps:
Toggle the option off and on again.
This seems to set the flag correctly and the search returns to the settings area!