Is suspect something along those lines caused the issue, although I thought forcing the Assistant to show up again (using command line: 'defaults delete com.runningwithcrayons.Alfred skipOnboardingV5') would solve it. On a second computer it picked up the correct Dropbox preferences without my intervention. Weird.
Works greats, except... how to "import" the v4 settings, web searches, snippets, workflows, etc. (basically everything)?
EDIT: Obviously, I'm an idiot. Looks like the (Dropbox) synced settings have to be enabled manually. After that, everything's fine.
This might be related in some twisted way: The blur setting doesn't work anymore. At all. Funny enough the effect is visible when taking a screenshot (in the resulting image file). After double checking the Alfred settings I now randomly get weird artifacts, too. But only in Alfred's search bar. And this time they don't appear in the screenshot, so I had to use my smartphone camera...
VLC is not running. I don't have Final Cut installed. Worked fine before the Catalina update.
MacOS Catalina 10.15 (19A583) Alfred 4.0.4 [1111] (Powerpack)