Hi there,
This is my idea. You need to create a new module to show it.
1. 1 file js, after loading product list page, it will get the all id products (you can get id_product by product url, data_idproduct, ...) of this page, after that use ajax >> sending this list id_product to front controller of module.
2. Front controller will get list id_product,
get the products in the current cart ($product = $this->context->cart->getProducts(true))
=> compare 2 arrays => product in cart
3. in function success of js, check and show the flag (already in cart)
Thanks,