After some January updates got the same problem, but on Ubuntu 18.10.
Reinstalling appindicator packages (see commands below), somehow partially fixed the problem: lang indicator stop disappearing in gnome-shell, but still do in gdm.
apt install --reinstall gir1.2-appindicator3-0.1
apt install --reinstall gnome-shell-extension-appindicator
the commands above didn't work. worked solution, at least for ubuntu 18.10 (Cosmic), is rollback to previous version of
sudo apt install --reinstall gnome-shell=3.30.1-2ubuntu1 gnome-shell-common=3.30.1-2ubuntu1
and perform the reboot
optionally, but highly recommend - prevent update on those packages, like these:
sudo apt-mark hold gnome-shell gnome-shell-common
and wait for fix. after fix will be released - just
unhold those packages and run update\upgrade command.
for ubuntu 18.04 (Bionic)
you should try rollback those packages to
possible origin of the problem
the only difference between old version and version at January update is in this bugfix; he also relate to ibus, so that fix may be the cause of the "disappearing lang indicator" problem