Hi,
Maybe I wasn't clear enough, but the stock of variants is not taken into account for the display of the product on the products listing. Only the stock of the main product is taken into account.
So it doesn't matter what stock you have in the variants, or if they are published or not.
I ran a test purchase with a stock of one, the variant stock got properly set to 0 but it's still showing in the product listing.
You need to look at the stock of the main product, not the stock of the variant.
And regarding the setting
System > main > product > "Show sold-out products"
that's the setting for new products listings. You need to edit the menu item via the Joomla menu manager and under the "products options" tab, you'll find an option with the same name. And that's this setting which is important to check.