After I’ve started AutoKey I can’t find it on my desktop

When AutoKey starts, it does not open a window unless this is your very first time running AutoKey, i.e., the ~/.config/autokey directory does not exist. Instead, it places an “A” icon in the system tray through which its main window and other functions can be accessed.

If you are a GNOME desktop user, your desktop may not have a system tray, so it may appear that nothing happened when you started AutoKey. To use AutoKey effectively, you should install a GNOME Shell extension that adds a system tray to your desktop. My personal favorite extension for this purpose is “AppIndicator and KStatusNotifierItem Support by 3v1n0,” but there are other choices. Ubuntu, for example, comes with the “Ubuntu Appindicators” extension already installed so this isn’t a problem there. Go to https://extensions.gnome.org to find, install, and manage GNOME Shell extensions on your desktop.