I am using the “Jace” theme, which I don’t believe is widely used. In any case, this theme seems to be relying on WooCommerce Blocks to list all the products on the shop page, which I believe uses AJAX to load the products. I tried every hook provided by your plugin and none of them worked for the shop page, probably because they rely on PHP hooks rather than AJAX.
I did, however, play with some JavaScript to show my own badge. Unlike the latest “Twenty Twenty…” themes provided by WordPress, the Jace theme fails to add an “outofstock” class for out of stock items, but it does change the “Add Item” button text to “Read More”, so I was able to look for that within a JavaScript “MutationObserver”.
Anyway, by the time I had the Shop page as I wanted it, I decided to add to my own custom plugin to take care of the single product page as well, which meant I didn’t need your plugin. However, I really liked your plugin and will consider it for other sites. As I said, it worked fine on the Twenty Twenty-Four, -Three and -Two themes, and it is easy enough for less-technical people to figure out.