greeter.py is hard to debug & looks in the wrong place for .desktop files.

[crabdancing]

greeter.py does a number of internal operations that are difficult to debug without modifying the script to introduce logging. It also (bizarrely) was looking in /usr/share/, but not /run/current-system/sw/share/. I'm not sure what could have possibly caused this, but I found that by patching it with an extra directory path improves robustness and should have no effect on any other systems for which the script was originally working.

See Matrix messages from here onward for the debugging process & details.