> On GNOME we already have a global shortcut for some emoji picker, I think it's Super + , or something
Actually, on most distros, the default keyboard shortcut for the emoji picker on GNOME/GTK is ctrl-. (same as the Firefox shortcut). This only works on apps that support it. Older Firefox versions did not support GNOME's emoji picker at all, but Firefox 150 supports GNOME's emoji picker using the expected keyboard shortcut.
Actually, on most distros, the default keyboard shortcut for the emoji picker on GNOME/GTK is ctrl-. (same as the Firefox shortcut). This only works on apps that support it. Older Firefox versions did not support GNOME's emoji picker at all, but Firefox 150 supports GNOME's emoji picker using the expected keyboard shortcut.