Through tips from @mladen experimentation, studying https://tracker.pureos.net/T486 and some evtesting on a working laptop, I was able to find a not so intuitive solution. evtest showed me that the the \-key sends code 0x56 and the #-key sends 0x2b. Creation of an override file /etc/udev/hwdb.d/90-purism-backslash-key-fix.hwdb with the following contents solved my problem:
evdev:atkbd:dmi:bvn*:bvr*:bd*:svnPurism:pnLibrem13v2*
KEYBOARD_KEY_56=KEY_102ND # The backslash key sends 0x56
KEYBOARD_KEY_2b=KEY_BACKSLASH # The hash sign key sends 0x2b
(No, the associations are not the wrong way around!)