You should already be able to implement Yotpo reviews/ratings widgets in your own site without requiring any particular integration support from us, since we are completely uninvolved in managing your site's layout and content. Unlike many of the other ecommerce platforms listed, we don't generate an entire site or an online storefront cataloging product listings for you, so integration at that level of things would be irrelevant to us and our clientele.
The only potential integration of any relevance in our case would be having us automatically notify Yotpo when a sale occurs, so they could email the buyer to request a review/rating. This would need to use our standard custom/third-party Integration feature, as linked above, so if Yotpo is uninterested in supporting that, we cannot make them support it.
The only third-party APIs we support would be for payment processing services, as that's strictly necessary to integrate with them for checkout at all. As a matter of policy, we do not ever support third-party APIs for post-checkout order processing needs; however, if the third party will not support our standard Integration method, you can hire a developer to write a "middleman" script that would receive our standard Integration transmissions and then retransmit that data to the third party by whatever means and in whatever format they require.