After modifying the Librem version to 3 in 90-purism-pipe-symbol-fix.hwdb file that ewout/quban specified, I was FINALLY able to get the keys to work properly in Qubes 4.0
Solution that worked for me:
Create /etc/udev/hwdb.d/90-purism-pipe-symbol-fix.hwdb with the content:
evdev:atkbd:dmi:bvn*:bvr*:bd*:svnPurism:pnLibrem13v3*
KEYBOARD_KEY_56=backslash
Run:
sudo systemd-hwdb update
sudo udevadm trigger
Notice that the file contents specifies pnLibrem13v3* not pnLibrem13v2*