A few things of note here:
Alfred runs as a user level process, and doesn't install any lower level OS based extensions, so isn't even capable of creating a kernel panic. This is unless one of the macOS APIs Alfred is using is bugged or corrupted, more likely the latter as this is the first mention of this I've heard.
There is no underlying rendering differences between 4.0.5 and 4.0.6, so I'm certain that the behaviour difference is purely coincidental.
A few users have seen graphics bugs in Catalina in both the Alfred window and the macOS dropdown and popup menus (where Alfred isn't installed) based around the window blur. If you select the Alfred Classic theme (or create a custom theme and set the window blur to 0), then this will rule out the blur causing a GPU issue.
Have you tried running on a new user account to rule out another underlying app (which you may not even know is installed) interfering with your Mac's operation.
Kernel panics are unusual, but Catalina is new and notoriously buggy still. If you upgraded via an old OS, or via the macOS Beta path, there may be an underlying OS corruption or misconfiguration. Are there other quirks you are experiencing on your Mac?
Cheers,
Andrew
