Dear Hardkorn, sorry - I didn’t want to be disrespectful. Now I reopened the Everything Options dialog and clicked the “Show Search Everything …” option, and it turned from indeterminate to checked:
And now Everything is shown in the background context menu:
It seems that, for some reason, this option had been in a kind of indeterminate or “suspended” state before. This can happen sometimes when an application can’t decide between two boolean states (true or false), for whatever internal reason that might be. (A checkbox can have 2 or 3 states, depending on how the developer of the application configures it. In this case, IMO the 2-states option would have been the better choice).
Anyway, I am happy that the question is now resolved. Thank you again for your screenshot, and sorry again for the misunderstanding.