xdotool works with Xorg only. There is an alternate tool,
ydotool that works at a lower level and thus functions in both Xorg an Wayland.
ydotool does not have the window manipulation options that
xdotool has, but supports simulating keyboard and mouse actions.
You can move to an Xorg session to continue working with
xdotool. If you prefer to stay on Wayland, you may want to move to
ydotool to preserve the functionality.
ydotool is available in the repositories of Ubuntu. However, even on 22.20, an old version is shipped that, for me, did not work. I therefore compiled it from source, and that is actually not so difficult. I documented the procedure on Ubuntu 22.04 here on the site.
Note that the new version is a very slimmed down version, reduced to core functionality. The new version also requires the daemon to be running. A drawback of the new version is that symbolic key presses do not work: you explicitly have to "press" and "release" keys yourself using numerical codes. As such, simulating Alt+Tab in
ydotool translates to:
ydotool key 56:1 15:1 15:0 56:0
(We press Alt, then Tab, then release Tab and Alt.)