GNOME's AppIndicator extension turns button-1 on the tray icon into a
StatusNotifierItem Activate() call, Qt re-emits it as activated(Trigger), and
nothing was connected to it — so the most obvious gesture on the one UI that is
meant to be reachable mid-set did nothing at all. Only button-3 opened anything,
and that menu is drawn by the shell from the exported DBusMenu, not by us.

Qt5 hardcodes ItemIsMenu=false, so the host will never open the menu for us on a
left click; popping it at the cursor is the only route. Middle click too — a
hidden third behaviour mid-set is worse than a redundant one.

popup(), not exec_(): exec_() spins a nested modal event loop, which would stall
the 2s refresh timer and the gearbox reads behind it for as long as the menu
stayed open.