As noticed on #12364#note-33, our own
config/gdm-shell-tails.desktop (in Tails Greeter's Git repo) tends to be behind
/usr/share/applications/org.gnome.Shell.desktop as shipped in Debian. This can potentially cause serious issues, so IMO we need a process to keep it more up-to-date than what we've done in the past. I don't know what's the best way to do that, but at least a ticket per Tails release based on the next version of Debian would be a good start; completing said ticket would require creating the next one. But there are probably better ways to do so, e.g. generate our own .desktop file dynamically at package build time from the upstream one.
gdm-tails.session, see f5e00d2d1051991e29720c422337e8855ca17cb2.