Build an API for a wordpress site that takes listings (text, photos ,custom fields) from a CRM and turns them into posts on the WP site

We run vertical-imob.ro, a real estate website. We have a CRM we use, it`s documentation can be found here: https://catalinux.github.io/realmanager-docs/. We`re looking to get a custom API built on our WP site that would sync all new listings from the CRM, grab the data (title, description, ID, photos, custom fields) and publish them as posts on our wordpress site. The posts need to be styled according to our theme.