Adding the last item to multiple carts not blocked

Hi there! I’m seeing some unexpected behaviour and wondering if this is a bug or just some setting I have managed to miss.

I have a product set up like this:
Track stock quantity? Yes
Quantity? 1
Allow backorders? No

I am able to add the product to my cart, then open an incognito window or a different browser and still add it to my cart.

If I proceed to checkout on one of them the quantity is updated to 0, and if I try to buy it twice I get an error. But how can I block the product from being added to the cart twice when the stock level is at one single item?

(I am on the newest versions of WooCommerce and WordPress.)