The Apple User Interfaces for connecting newly updated Apple Devices are confounding.
Say you have two macs and an iPhone or two… after upgrading the OS it needs another device already acknowledged as yours to approve things – it locks the screen form with a spinning icon waiting for the aforementioned approval. However that screen has no entry field to enter the authenticating code sent to the existing device – it is locked.
You are not told on which device the authentication protocol has been initiated.
Quite possibly it is busy downloading the same update there that got you into this quandary? Furthermore you need to enter your rather long password suffixed with the new code – and inadequate time is allowed to do this. Even if you turn off all other devices but one to limit the ambiguity of where to look, it then wants passwords to the turned off devices! Why? Particularly if you do not wish to use iCloud Drive, but just use the basic synchronised Contacts, Calendar, Notes and iMessage infrastructure. Furthermore, the authenticating codes to be entered sometimes come up in quick succession with no clue as to which device they are to be entered! Bear in mind that updates often are happening on multiple devices so this confusion is real.
All to easily, you find yourself in a catch twenty two situation whereby more than one device is waiting on another so resolution is a challenge!
Clearly, you need to get one connected to the cloud before upgrading and connecting the next, but there is nothing enforcing or facilitating that. Sometimes waiting helps, but this dilemma needs to be fixed by a rethought overarching strategy at Apple – after all do they not want families to buy multiple Apple devices?