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On X11 and the Fascists Maggots
(blogs.gnome.org)
A community for everything relating to the GNU/Linux operating system (except the memes!)
Also, check out:
Original icon base courtesy of lewing@isc.tamu.edu and The GIMP
I don't know autokey, so I can't speak to whether they replace all its functionality but there are 'xdotool-like' programs for Wayland. So it is at least very possible to replace functionality like the latter you mentioned (press button/button combination -> do an action, like inserting date/start a program/do something programmatic). Some examples I know are:
ydotool is a perfect replacement for dmenu based password managers.