Hi @b1026q9
Thank you for providing the screenshot, this is really helpful! ??
I replicated the scenario on my test site using one of the variable product, however, I was not able to reproduce the issue. The Out of Stock notification is displayed on my end and the Add to Cart button is disabled as well.

Image Link: https://snipboard.io/hMzHUs.jpg
Meanwhile, I was not able to test this on your site since the site URL was not the actual URL of your site.
Can you please try to switch to the default Storefront theme and only WooCommerce plugin is enabled and see if this works?
If so, then, please try to perform a full conflict test to check what causes the conflict on your site, either a third-party plugin, your theme, or any custom code present on your site.
https://woocommerce.com/document/how-to-test-for-conflicts/
If this was caused by a third-party plugin present on your site, it would be best to reach out to the developers for further assistance here.
Let us know how it goes!