Enabling this option https://prnt.sc/T4VmfgFplBH8 is required to show X on out of stock variations.
We do not know why it work on https://sochic.com.ar/shop/pantalon-kim/ , but it is not predefined behavior from our theme side there.
Sorry, but we can’t give you a solution for https://hamaratadenim.com.ar/ , because it works fine – according to predefined in the theme behavior.
You need to find out how you achieve the desired work on the sochic.com.ar site and repeat it on another site, but we can’t assist you because of the previously mentioned reason, unfortunately.
One standard license is valid only for 1 project. Running multiple projects on a single license is a copyright violation.