I tried the v1.8.0-alpha on Ubuntu 20.04 (using the Zettlr-1.8.0-alpha-amd64.deb). It installed without problems (using gdebi package installer). However, doesn't show up in the list of applications or when searching for it.
I don't know why it doesn't show up, but there was a small bug in the desktop file, which has been fixed.
OK, that sounds like that might have been the problem. I'll try it out when back behind my computer. Thanks