I have a 2019 iMac 27 and a 2019 iMacPro that are both showing in Settings/Overview "Update Apple ID Settings". When I select Continue and then Continue on the Update Apple ID Settings, I am asked for the password used to unlock this Mac. It just remains on the same panel that was originally displayed.
I have found this was an issue in earlier 10.15 betas and I have checked that I can log on to Podcasts, Music and TV which seemed to be the most common fix. I can log oout and back in to all of these apps, without correcting the outstanding Update Apple ID Settings.