As a windows guy taking a stab at it… the export profiles are hard coded and then any that you add go in a folder in the config folder of DT color/out… that folder looks like it might be a location for display profiles but maybe not for export… you might even have to create that folder at least in windows I dont’ think its there by default…
If you put it in the location you listed, it’ll be wiped out on the next update.
The darktable flatpak keeps its user settings in ~/.var/app/org.darktable.Darktable/ so color profiles go in ~/.var/app/org.darktable.Darktable/config/color/out for output profiles. (This was off the top of my head, but should be close). Conversely there should be an in folder for input profiles. Create the folders if necessary.