In Ventura (13.2), you can turn off automatic updates in the “General” tab, then “Software Update” and click on the little “(i)” icon to the right of “Automatic updates”.

When I saw it the first time, it was unclear to me that I can even click on it, since it doesn’t look much like a button. They shouldn’t hide such important settings in a tiny icon or at least should have made it much more apparent that it is clickable.

Couldn’t find any settings related to the closed lid though.