I have installed Thunderbird 78.5.1-0.1 on a brand new deployment of Manjaro 20.2 Gnome and I cannot see a badge on Thunderbird icon when I have new / unread e-mail.
Switched from Dash to Dock to Dash to Panel, KStatusNotifierItem/AppIndicator Support Gnome Extension is enabled - nope, no badge.
After some searching there seems to be mixed ways to get something similar by using external tools, e.g. SysTray-X or Gnome extension New Mail Indicator (both not working for me) or BirdTray (works, but hard to notice new message count, until you make it flashy).
How can I get that working without using external tools - this feels like I have missed something basic in the first place, for such a QoL setting?
For example, on my main PC I use Geary and badge is working out-of-the-box.