I understand and appreciate your approach. Mine was exactly the same.
Doing a cold reboot of a system during an OS upgrade, is normally high risk, based on my background.
Regarding you queries:-
a) What could be causing the issues?
Ans - This is an Apple only possible response. Catalina was only released formally in the last 48hrs or so.
b) Whether rebooting is actually necessary, i.e., will "setting up..." perhaps eventually complete if I wait long enough?
Ans - I waited between 3-4hrs or more. I did not use a stop watch. I fortunately was on my Mac mini when I started the MacBook update. My trusted MackBook pro has been very quick with 16Gb of ram and a brand new 1Tb ssd drive.