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:

• wtype
• wlrctl
• swhkd
• ydotool