My MBP was upgraded to Catalina 10.15 several months ago and I almost did not encounter any issue until I found the further update 10.15.1.
Following the instruction I downloaded the update and rebooted, then waited for several minutes ( in fact such update usually will take about half hour) and I entered the system while just found nothing happened. I still got the icon that I got a system update!
The same thing continued on 10.15.2 and the latest 10.15.3.
I could not find any helpful message and also could not get any help from Google search. I read plenty of notes while none of them worked.
So I decided to reinstall the whole system while kept all my applications and data so such installation will just like a update.
Below web page gave me the keys I should press during the reboot:
To install the latest update, I selected the second option (Option-⌘-R) then followed the prompt to select my account, choose the harddisk and unlock it, then wait for a longer time like half hour.
Finally I entered my system again and all my things were still there and the system was the latest 10.15.3.
This issue confused me for several months and I thought maybe the update program has some issues as I did not get prompt to unlock the harddisk when I installed the update directly, while the reinstall did give me such prompt.