In order to display the SKU of the selected product, you can create a Plugin (Interceptor) for Magento\ConfigurableProduct\Block\Product\View\Type\Configurable::getJsonConfig()
where you need to add missing SKU for each simple product. Out of the box, when choosing options, images, price, etc will change, but not SKU.
The SKU obtained with getJsonConfig()
can be updated in the frontend when selecting an option in vendor/magento/module-swatches/view/base/web/js/swatch-renderer.js
or/and vendor/magento/module-configurable-product/view/frontend/web/js/configurable.js
depending on the type of attribute (Dropdown, Visual Swatch, Text Swatch).
I made free VCT Change SKU Dynamically
module that solve this problem.