Dropbox does not yet support macOS Catalina (10.15) and won't until its final, stable release. You may be able to install Dropbox on it but you're bound to run into issues until Dropbox officially supports it.
I would uninstall and reinstall it... Catalina has new file access permissions for each time an app wants to access somewhere it hasn't before... failing that check the permissions for dropbox under system preferences and make sure it has full disk access.
I carried out your two suggestions sequentially, each time rebooting my computer. Neither worked by itself nor in combination.
So, I went back in to "Full Disk Access" list and removed Dropbox from the approved list. As an aside, Google Drive was unaffected by the current Catalina build and did not require Full Disk Access.
I examined the list of apps under "Accessibility" and Dropbox was enabled for that function.
Thanks so much for your suggestions, though. In the process, I did re-learn that uninstalling and re-installing is in fact different from merely deleting the desktop app and re-installing.
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