Stephanie here from Shopify.
We have a doc that includes a step by step guide to add a message when a product is out of stock! Here's the direct link - https://help.shopify.com/manual/products/inventory/product-availability?utm_medium=Forum&utm_campaig...
Hope this helps! :)
We are using an older theme, Minimal, that is supported by Shopify. I contacted them and they added a badge "Sold Out" similar to the Sale badge. It automatically shows when inventory is out. You can see it at the bottom of our page shop.daskeyboard.com.
Hope this helps
We also need this feature. I just had Chat conversation with Shopify team and they give standard reply: " this is not a feature we currently offer. I can certainly put in a request to have this feature added... I will send this up to our development team. The more requests that are received for a feature like this, the more likely it is to be developed. It can take quite some time before a request is actioned. New features are usually updated on the Shopify Blog."
And now we wait ;)
Some tweaks to the theme would be an option. Is that not a path you can take? The theme determines the UI that the customer sees.
If all the products have the same replenishment time it's easier.