Latest findings: One of the files that “apt install kubuntu-settings-desktop” creates is
/etc/fonts/conf.avail/56-kubuntu-noto.conf
If I rename that file from .conf (e.g.) .conf.IGNORE (or move it away or delete it…) then
drumroll
the AppImage looks nice again. The nice font is used and the icons appear 
Tried the same on my real/live system: UI looks nice again, too.
I currently don’t know what is getting worse elsewhere by disabling this font configuration.