Surprisingly, customers need to click on the product page and scroll all the way to the bottom of the page (I have long descriptions too) in order to see that a product has sold out.
So I would imagine most customers are looking through the product photos and reading the description, thinking about whether to purchasing it and finally deciding on "yes, I'll purchase it!" then they scroll down to add it to their cart to finally see the tiny 'Sold Out' text need the 'Add to Cart' button.
What would be much more convenient for prospective customers is to add a 'Sold Out' banner to the thumbnail image of the product that sells out or text above or below the pricing/title.
Please consider adding this feature. It's a very common feature most website platforms have. I was surprised when I joined Weebly and saw that this wasn't a thing.