@Moini was right: Opening a ticket on the Inkscape bugtracker was a good and Nathan Lee replied quickly.
I sum up the answer for the other .sx readers, because I expect that several systems need fixes in order to prevent duplicate or wrong paths:
Inkscape uses the paths returned by
Glib::get_system_data_dirs
and
Gtk::IconTheme::get_default()->get_search_path()
.
These can be collected on the command line via
python3 -c "from gi.repository import GLib; print(GLib.get_system_data_dirs())"
['/usr/local/share', '/usr/share', '/usr/share']
python3 -c "from gi.repository import Gtk; print(Gtk.IconTheme.get_default().get_search_path())"
['/home/myuser/.local/share/icons', '/home/myuser/.icons',
'/usr/local/share/icons', '/usr/share/icons', '/usr/share/icons',
'/usr/local/share/pixmaps', '/usr/share/pixmaps', '/usr/share/pixmaps']