The issue is with a fresh installation of Ubuntu 18.04 using the default GNOME Desktop. The “tray icons” simply don’t appear in the top panel. “Ubuntu appindicators” shell extension is active, but doesn’t show any icons. If you’ve tried both the “kstatusnotifieritem” and “topicons” shell extensions without any success the this will help.
sudo apt purge indicator-common
If you don’t have it already, install the package
gnome-tweaks. To install package type:
sudo apt-get install chrome-gnome-shell
Then search and install either the TopIconsPlus or Ubuntu AppIndicators extension, and reboot the system.
Then you would be able to see the icons on the GNOME’s bar. Instead of rebooting, you could just reload the Gnome Shell: press Alt+F2, enter R, and press Enter.