telegram-desktop installed via
pacman on the Arch Linux.
After starting – no systray’s icon present and thus can’t see new messages and even can’t exit in a normal way.
This issue is not specific for the Arch Linux and happens on any Linux systems.
Go to the Google and make search with “telegram linux no systray” – the very first result will lead you to the 2017’s year
So the solution is just to install the