Found the solution by adding this code to the theme product listing phtml file.
<div class="field qty">
<!-- <label class="label" for="qty"...
On a quick thought on the matter, this looks like a normal behavior.
When you are accessing the browser, you are basically just another guest user, who will generate another cart ID and not the one you added from your api call.
I don't think that you can simply load another user's cart by its ID, since this is a matter of private content and the whole ...
You can use this api to check whether the product has been added to the cart or not. If the api returns the correct cart and the product you added earlier please clear the cache and try again.