I'm astonished that it still has this issue in 2019 with macOS Catalina, Serif team should definitely take care of the permission issue with macOS update. Here's the workaround:
Open your System Preferences - Security & Privacy.
Click the lock icon on the lower-left corner to unlock this pane
Navigate to Full Disk Access on the left sidebar
Click the “+” icon to add Affinity Design/Photo to the list
Restart your Affinity Design/Photo app