It shows up well on my cart page but it does not connect with my store shipping price at the backend; (customers don’t get free shipping when they reach the threshold)
To add the simple shipping progress bar to your cart page you can use the iCart Cart Drawer Cart Upsell app, this app is free to use up to 50 orders per month.
Another option, if you didn’t want to use an app you could create a free shipping rate in Shopify. That way you could use your original solution to power the in-cart AOV prompt, and let Shopify’s native settings handle applying the rule.