Hello,
When I add an item to my wishlist and then I set this item to Private, it will no longer appear in the wish list but the basket still shows 1 article.
is there a way to display the articles anyway, or to set the basket to zero?
Please deactivate all the plugins not related to the theme and switch the parent theme, check the issue, If the problem has gone, activate the plugins one by one, checking the issue to detect which one causes the problem.
if you later set some products to invisible (Private) that the season is over..the wishlist still shows the number of products in the header, although they can no longer be seen in the list itself
The situation you describe is not applicable in the real life. A store buyer does not have the option to hide the product in admin.
As soon as the product has been hidden, it is not possible to view it and add it to the Wishlist.
From the other side, the Wishlist should keep the product data for some time other wise there is no sense in the Wishlist.