Out of Stock Label on Products Thumbnail and product page

It would be very helpful if products that are out of stock—but not marked as "Closing Out"—automatically display a “Sold Out” or “Out of Stock” label on both the product thumbnail and the product page.

Currently, when "Closing Out" is checked, the product disappears from the listing once it runs out of stock. However, we prefer not to use this setting, as we want to be able to restock the item later via a PO, not manually through the backend page.

Without the “Closing Out” option enabled, out-of-stock products remain visible in the listing, but there's no easy way to tell that they’re unavailable. While we can click through to view inventory if the option is on, it requires several steps. A visible “Out of Stock” label would provide a much clearer user experience and is a standard feature on most e-commerce platforms today.

Shopify Examples: