Thank you for your thoughts, Peter_Watt. I tried them but had no success, so I started poking around to see what I could do that would change the symptom.
To recap, the original issue was that after MacOS 10.15 was installed, it broke my Notecase installation. Specifically, Notecase was denied permission to my Documents folder, where I kept all my Notecase docs. That made it unusable. I called Apple support but got little help there beyond the standard level 1 support suggestions - run AV check, update the app, check with Notecase to see if they didn't support this release of the OS, etc. Apple also had me do a couple of unusual things - reset the System Management Controller and reset NVRAM or PRAM. And of course, I updated the Mac to the 10.15.2 just to make sure there were no new fixes out there.
I then looked at permissions for my home folder, my Documents folder, and my Documents/Notecase folder but didn't change them. Given that other apps were able to browse those same folders, I didn't feel like permissions were the issue here.
I then started poking around from Notecase to see if there were any folders it COULD see. Turns out that there is a hidden folder called .Notecase that it could get into. I copied one of my files to that folder and Notecase was able to open it and work with it again. So, the immediate issue is resolved -- worked, around, actually.
However, I would very much like to know what Apple changed from 10.14 to 10.15 that caused this issue.