What this suggests to me (I'm guessing here, hoping someone can help
me figure it out) is that YAD is compiled with GTK support on Debian
and Fedora, but some other graphical library on the Pi.
Seems to be built with GTK support here (Raspberry Pi 4):
ldd /usr/bin/yad | grep -i gtk
libgtk-3.so.0 => /usr/lib/arm-linux-gnueabihf/libgtk-3.so.0
Touch screens - especially small ones - aren't very useful on a Raspberry Pi. X is really hard to make tiny, and there isn't any actively-maintained non-X thing.